To simplify the expression 24 ⋅22 using the product rule of exponents, we add the exponents together:
24 ⋅ 22 = 2^4 ⋅ 2^2 = 2^(4+2) = 2^6
So, 24 ⋅22 simplifies to 2^6.
Use the Product Rule of Exponents to simplify the expression 24 ⋅22 .
44 answers
Question
Use the Product Rule of Exponents to simplify the expression 3
6^8 ⋅3^3 .
Use the Product Rule of Exponents to simplify the expression 3
6^8 ⋅3^3 .
To simplify the expression 6^8 ⋅ 3^3 using the product rule of exponents, we add the exponents together:
6^8 ⋅ 3^3 = (2^3)^8 ⋅ 3^3 = 2^(3*8) ⋅ 3^3 = 2^24 ⋅ 3^3
So, 6^8 ⋅ 3^3 simplifies to 2^24 ⋅ 3^3.
6^8 ⋅ 3^3 = (2^3)^8 ⋅ 3^3 = 2^(3*8) ⋅ 3^3 = 2^24 ⋅ 3^3
So, 6^8 ⋅ 3^3 simplifies to 2^24 ⋅ 3^3.
Use the Product Rule of Exponents to simplify the expression 75 ⋅72
To simplify the expression 75 ⋅ 72 using the product rule of exponents, we need to rewrite the numbers in terms of their prime factorization:
75 = 3^1 ⋅ 5^2
72 = 2^3 ⋅ 3^2
Now we can use the product rule of exponents to simplify:
75 ⋅ 72 = (3^1 ⋅ 5^2) ⋅ (2^3 ⋅ 3^2)
Since the bases are different (3 and 2), we cannot simplify further using the product rule of exponents. Therefore, the expression 75 ⋅ 72 cannot be further simplified.
75 = 3^1 ⋅ 5^2
72 = 2^3 ⋅ 3^2
Now we can use the product rule of exponents to simplify:
75 ⋅ 72 = (3^1 ⋅ 5^2) ⋅ (2^3 ⋅ 3^2)
Since the bases are different (3 and 2), we cannot simplify further using the product rule of exponents. Therefore, the expression 75 ⋅ 72 cannot be further simplified.
Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
(52)9
left parenthesis 5 squared right parenthesis superscript 9 baseline
62⋅73
6 squared times 7 cubed
108⋅108
10 superscript 8 baseline times 10 superscript 8 baseline
327
Responses
(52)9
left parenthesis 5 squared right parenthesis superscript 9 baseline
62⋅73
6 squared times 7 cubed
108⋅108
10 superscript 8 baseline times 10 superscript 8 baseline
327
The expression that is correctly developed to use the Product Rule of Exponents is 62⋅73 (6 squared times 7 cubed).
Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses
10015
100 superscript 15 baseline
10056
100 superscript 56 baseline
20015
200 superscript 15 baseline
10,00015
Responses
10015
100 superscript 15 baseline
10056
100 superscript 56 baseline
20015
200 superscript 15 baseline
10,00015
To simplify the expression 1008⋅1007 using the Product Rule of Exponents, we add the exponents together:
1008 = 2^4 ⋅ 3^2 ⋅ 7^1
1007 = 2^0 ⋅ 3^0 ⋅ 7^1
By multiplying the bases together separately, we can use the Product Rule of Exponents:
1008⋅1007 = 2^4 ⋅ 2^0 ⋅ 3^2 ⋅ 3^0 ⋅ 7^1 ⋅ 7^1 = 2^(4+0) ⋅ 3^(2+0) ⋅ 7^(1+1) = 2^4 ⋅ 3^2 ⋅ 7^2
Therefore, the correct expression that uses the Product Rule of Exponents to simplify 1008⋅1007 is 20015 (200 superscript 15 baseline).
1008 = 2^4 ⋅ 3^2 ⋅ 7^1
1007 = 2^0 ⋅ 3^0 ⋅ 7^1
By multiplying the bases together separately, we can use the Product Rule of Exponents:
1008⋅1007 = 2^4 ⋅ 2^0 ⋅ 3^2 ⋅ 3^0 ⋅ 7^1 ⋅ 7^1 = 2^(4+0) ⋅ 3^(2+0) ⋅ 7^(1+1) = 2^4 ⋅ 3^2 ⋅ 7^2
Therefore, the correct expression that uses the Product Rule of Exponents to simplify 1008⋅1007 is 20015 (200 superscript 15 baseline).
Find the numerical equivalent of 102 ⋅103(1 point)
Responses
100,000
100,000
105
10 superscript 5 baseline
10
10
1,100
Responses
100,000
100,000
105
10 superscript 5 baseline
10
10
1,100
To find the numerical equivalent of 102 ⋅ 103, we simply multiply the two numbers together:
102 ⋅ 103 = 100 ⋅ 1,000 = 100,000
Therefore, the numerical equivalent of 102 ⋅ 103 is 100,000.
102 ⋅ 103 = 100 ⋅ 1,000 = 100,000
Therefore, the numerical equivalent of 102 ⋅ 103 is 100,000.
Find the numerical equivalent of 25 ⋅2−2(1 point)
Responses
128
128
8
8
2
2
16
Responses
128
128
8
8
2
2
16
To find the numerical equivalent of 25 ⋅ 2^(-2), we evaluate the expression by simplifying the exponent:
2^(-2) is the same as 1 / 2^2, which equals 1 / 4 or 1/4.
Now we multiply 25 by 1/4:
25 * 1/4 = 25/4
Therefore, the numerical equivalent of 25 ⋅ 2^(-2) is 25/4.
2^(-2) is the same as 1 / 2^2, which equals 1 / 4 or 1/4.
Now we multiply 25 by 1/4:
25 * 1/4 = 25/4
Therefore, the numerical equivalent of 25 ⋅ 2^(-2) is 25/4.
Find the numerical equivalent of 49⋅4−7(1 point)
Responses
416
4 superscript 16 baseline
16
16
42
4 squared
4
Responses
416
4 superscript 16 baseline
16
16
42
4 squared
4
To find the numerical equivalent of 49 ⋅ 4^(-7), we evaluate the expression by simplifying the exponent:
4^(-7) is the same as 1 / 4^7, which equals 1 / 16384 or 1/16384.
Now we multiply 49 by 1/16384:
49 * 1/16384 ≈ 0.00299
Therefore, the numerical equivalent of 49 ⋅ 4^(-7) is approximately 0.00299.
4^(-7) is the same as 1 / 4^7, which equals 1 / 16384 or 1/16384.
Now we multiply 49 by 1/16384:
49 * 1/16384 ≈ 0.00299
Therefore, the numerical equivalent of 49 ⋅ 4^(-7) is approximately 0.00299.
Simplify this expression using the Quotient Rule of Integer Exponents: t400t100.(1 point)
Responses
300
300
t300
t superscript 300 baseline
t4
t superscript 4 baseline
t500
Responses
300
300
t300
t superscript 300 baseline
t4
t superscript 4 baseline
t500
To simplify the expression t^400 / t^100 using the Quotient Rule of Integer Exponents, we subtract the exponents:
t^400 / t^100 = t^(400 - 100) = t^300
Therefore, the simplified expression using the Quotient Rule of Integer Exponents is t^300.
t^400 / t^100 = t^(400 - 100) = t^300
Therefore, the simplified expression using the Quotient Rule of Integer Exponents is t^300.
Simplify a67b34.(1 point)
Responses
23
23
a67b34
Start Fraction a superscript 67 baseline over b superscript 34 baseline End Fraction
ab33
a b superscript 33 baseline
a33
Responses
23
23
a67b34
Start Fraction a superscript 67 baseline over b superscript 34 baseline End Fraction
ab33
a b superscript 33 baseline
a33
The expression a^67b^34 cannot be simplified further or written in another form. Therefore, the simplified expression is still a^67b^34.
Apply the Quotient Rule of Integer Exponents to simplify 2365÷2332.(1 point)
Responses
2397
23 superscript 97 baseline
97
97
133
1 superscript 33 baseline
2333
Responses
2397
23 superscript 97 baseline
97
97
133
1 superscript 33 baseline
2333
To apply the Quotient Rule of Integer Exponents to simplify 2365 ÷ 2332, we subtract the exponents:
2365 ÷ 2332 = 2^(365 - 332) = 2^33
Therefore, the simplified expression using the Quotient Rule of Integer Exponents is 2^33.
2365 ÷ 2332 = 2^(365 - 332) = 2^33
Therefore, the simplified expression using the Quotient Rule of Integer Exponents is 2^33.
Simplify this expression using the Quotient Rule of Integer Exponents: 1253÷753.(1 point)
Responses
12106
12 superscript 106 baseline
553
5 superscript 53 baseline
1253÷753
12 superscript 53 baseline divided by 7 superscript 53 baseline
5106
Responses
12106
12 superscript 106 baseline
553
5 superscript 53 baseline
1253÷753
12 superscript 53 baseline divided by 7 superscript 53 baseline
5106
To simplify the expression 1253 ÷ 753 using the Quotient Rule of Integer Exponents, we subtract the exponents:
1253 ÷ 753 = 5^(253 - 53) = 5^200
Therefore, the simplified expression using the Quotient Rule of Integer Exponents is 5^200.
1253 ÷ 753 = 5^(253 - 53) = 5^200
Therefore, the simplified expression using the Quotient Rule of Integer Exponents is 5^200.
Which are the correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents?(1 point)
Responses
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Responses
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are different; if they are, subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Check if the bases are the same; if they are, add the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Subtract the exponents of the numerator and denominator; and write the resulting expression in exponential form.
The correct steps to follow to simplify an exponential expression using the Quotient Rule of Integer Exponents are:
1. Check if the bases are the same. If they are, subtract the exponents of the numerator and denominator (leave as-is otherwise).
2. Write the resulting expression in exponential form.
So the correct response is: Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
1. Check if the bases are the same. If they are, subtract the exponents of the numerator and denominator (leave as-is otherwise).
2. Write the resulting expression in exponential form.
So the correct response is: Check if the bases are the same; if they are, subtract the exponents of the numerator and denominator (leave as-is otherwise); and write the resulting expression in exponential form.
Which of the following is developed to result in the answer of 1?(1 point)
Responses
50+90
5 superscript 0 baseline plus 9 superscript 0 baseline
13−(7.42)0
13 minus left parenthesis 7.42 right parenthesis superscript 0 baseline
(−2.97)0
left parenthesis negative 2.97 right parenthesis superscript 0 baseline
3(80)
Responses
50+90
5 superscript 0 baseline plus 9 superscript 0 baseline
13−(7.42)0
13 minus left parenthesis 7.42 right parenthesis superscript 0 baseline
(−2.97)0
left parenthesis negative 2.97 right parenthesis superscript 0 baseline
3(80)
The expression that is developed to result in the answer of 1 is (−2.97)^0. According to the rule that any non-zero base raised to the power of 0 is equal to 1, the expression (-2.97)^0 is equal to 1.
Which of the following shows the correct process of solving −30+4.5?(1 point)
Responses
−30+4.5=(−3)0+4.5=1+4.5=5.5
negative 3 superscript 0 baseline plus 4.5 equals left parenthesis negative 3 right parenthesis superscript 0 baseline plus 4.5 equals 1 plus 4.5 equals 5.5
−30+4.5=−1⋅30+4.5=−1⋅1+4.5=−1+4.5=3.5
negative 3 superscript 0 baseline plus 4.5 equals negative 1 times 3 superscript 0 baseline plus 4.5 equals negative 1 dot 1 plus 4.5 equals negative 1 plus 4.5 equals 3.5
−30+4.5=−3⋅0+4.5=0+4.5=4.5
negative 3 superscript 0 baseline plus 4.5 equals negative 3 times 0 plus 4.5 equals 0 plus 4.5 equals 4.5
−30+4.5=−3+4.5=1.5
Responses
−30+4.5=(−3)0+4.5=1+4.5=5.5
negative 3 superscript 0 baseline plus 4.5 equals left parenthesis negative 3 right parenthesis superscript 0 baseline plus 4.5 equals 1 plus 4.5 equals 5.5
−30+4.5=−1⋅30+4.5=−1⋅1+4.5=−1+4.5=3.5
negative 3 superscript 0 baseline plus 4.5 equals negative 1 times 3 superscript 0 baseline plus 4.5 equals negative 1 dot 1 plus 4.5 equals negative 1 plus 4.5 equals 3.5
−30+4.5=−3⋅0+4.5=0+4.5=4.5
negative 3 superscript 0 baseline plus 4.5 equals negative 3 times 0 plus 4.5 equals 0 plus 4.5 equals 4.5
−30+4.5=−3+4.5=1.5
The correct process of solving −30 + 4.5 is:
−30 + 4.5 = −3 + 4.5 = 1.5
Therefore, the correct response is −30 + 4.5 = −3 + 4.5 = 1.5.
−30 + 4.5 = −3 + 4.5 = 1.5
Therefore, the correct response is −30 + 4.5 = −3 + 4.5 = 1.5.
Which of the following is an equivalent expression to 7(−5.3)0+4⋅9 when applying the Zero Power Rule? (1 point)
Responses
75.30+36
Start Fraction 7 over 5.3 superscript 0 baseline End Fraction plus 36
70+4⋅9
Start Fraction 7 over 0 End Fraction plus 4 times 9
71+4⋅9
Start Fraction 7 over 1 End Fraction plus 4 times 9
75.3+4⋅9
Responses
75.30+36
Start Fraction 7 over 5.3 superscript 0 baseline End Fraction plus 36
70+4⋅9
Start Fraction 7 over 0 End Fraction plus 4 times 9
71+4⋅9
Start Fraction 7 over 1 End Fraction plus 4 times 9
75.3+4⋅9
When applying the Zero Power Rule, any non-zero base raised to the power of 0 is equal to 1. Therefore, an equivalent expression to 7(−5.3)^0 + 4⋅9 would be:
7(−5.3)^0 + 4⋅9 = 7(1) + 4⋅9
Since anything multiplied by 1 does not change the value, this simplifies to:
7 + 4⋅9
So, the correct response is: 7 + 4⋅9.
7(−5.3)^0 + 4⋅9 = 7(1) + 4⋅9
Since anything multiplied by 1 does not change the value, this simplifies to:
7 + 4⋅9
So, the correct response is: 7 + 4⋅9.
Which of the following is an equivalent expression to 12(9−70)+(−29)0? (1 point)
Responses
12(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
12(2)+1
Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1
12(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0
12(9−1)+1
Responses
12(9−1)−1
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 1 right parenthesis minus 1
12(2)+1
Start Fraction 1 over 2 End Fraction left parenthesis 2 right parenthesis plus 1
12(9−0)+0
Start Fraction 1 over 2 End Fraction left parenthesis 9 minus 0 right parenthesis plus 0
12(9−1)+1
To find an equivalent expression to 12(9−70)+(−29)^0, we can simplify it using the Zero Power Rule which states that any non-zero base raised to the power of 0 is equal to 1:
12(9−70)+(−29)^0 = 12(-61) + 1
Now, we can simplify further:
12(-61) + 1 = -732 + 1 = -731
Therefore, the equivalent expression to 12(9−70)+(−29)^0 is -731.
12(9−70)+(−29)^0 = 12(-61) + 1
Now, we can simplify further:
12(-61) + 1 = -732 + 1 = -731
Therefore, the equivalent expression to 12(9−70)+(−29)^0 is -731.
Which of the following shows the correct process of solving −4(3+120)+150 by generating an equivalent expression using the Zero Power Rule? (1 point)
Responses
−4(3+120)+150 =−4(15)+15=−60+15=−45
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 4 times 5 equals negative 20
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 16 plus 1 equals negative 15
−4(3+120)+150=−4(15)+1=−60+1=−59
Responses
−4(3+120)+150 =−4(15)+15=−60+15=−45
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 15 right parenthesis plus 15 equals negative 60 plus 15 equals negative 45
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−4⋅5=−20
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 4 times 5 equals negative 20
−4(3+120)+150=−4(3+1)+1=−4⋅4+1=−16+1=−15
negative 4 left parenthesis 3 plus 12 superscript 0 baseline right parenthesis plus 15 superscript 0 baseline equals negative 4 left parenthesis 3 plus 1 right parenthesis plus 1 equals negative 4 times 4 plus 1 equals negative 16 plus 1 equals negative 15
−4(3+120)+150=−4(15)+1=−60+1=−59
To solve the expression −4(3+120)+150 and generate an equivalent expression using the Zero Power Rule, we simplify the expression inside the parentheses, perform the multiplication, and then perform the addition:
−4(3+120)+150 = −4(123) + 150 = -492 + 150 = -342
Therefore, the correct response is: −4(3+120)+150 = -4(123) + 150 = -342.
−4(3+120)+150 = −4(123) + 150 = -492 + 150 = -342
Therefore, the correct response is: −4(3+120)+150 = -4(123) + 150 = -342.
1 of 51 of 5 Items
Question
Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses
(78)⋅(710)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis
(−5)0
left parenthesis negative 5 right parenthesis superscript 0 baseline
129
12 superscript 9 baseline
(74)8
Question
Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses
(78)⋅(710)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis
(−5)0
left parenthesis negative 5 right parenthesis superscript 0 baseline
129
12 superscript 9 baseline
(74)8
The expression that is correctly developed to use the Power Rule of Exponents is (7^8) ⋅ (7^10) = (7^(8+10)) = 7^18.
Which of the following correctly used the Power Rule of Exponents in the expression (109)7?(1 point)
Responses
907
90 superscript 7 baseline
102
10 superscript 2 baseline
1063
10 superscript 63 baseline
1016
Responses
907
90 superscript 7 baseline
102
10 superscript 2 baseline
1063
10 superscript 63 baseline
1016
To correctly use the Power Rule of Exponents in the expression (10^9)^7, we multiply the exponents:
(10^9)^7 = 10^(9*7) = 10^63
Therefore, the correct response is 10^63 (10 superscript 63 baseline).
(10^9)^7 = 10^(9*7) = 10^63
Therefore, the correct response is 10^63 (10 superscript 63 baseline).
If the expression 410 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses
(45)2
left parenthesis 4 superscript 5 baseline right parenthesis squared
(412)2
left parenthesis 4 superscript 12 baseline right parenthesis squared
(42)8
left parenthesis 4 squared right parenthesis superscript 8 baseline
4⋅4⋅4⋅4⋅4⋅4⋅4
Responses
(45)2
left parenthesis 4 superscript 5 baseline right parenthesis squared
(412)2
left parenthesis 4 superscript 12 baseline right parenthesis squared
(42)8
left parenthesis 4 squared right parenthesis superscript 8 baseline
4⋅4⋅4⋅4⋅4⋅4⋅4
If the expression 410 was simplified using the Power Rule of Exponents, an equivalent expanded expression would be 4⋅4⋅4⋅4⋅4⋅4⋅4, which is the result of multiplying 4 by itself 10 times.
Use the Power Rule of Exponents to create an expression equivalent to (156)2.(1 point)
Responses
1512
15 superscript 12 baseline
153
15 cubed
158
15 superscript 8 baseline
154
Responses
1512
15 superscript 12 baseline
153
15 cubed
158
15 superscript 8 baseline
154
To create an expression equivalent to (15^6)^2 using the Power Rule of Exponents, we multiply the exponents:
(15^6)^2 = 15^(6*2) = 15^12
Therefore, the equivalent expression is 15^12 (15 to the power of 12).
(15^6)^2 = 15^(6*2) = 15^12
Therefore, the equivalent expression is 15^12 (15 to the power of 12).
What exponent would make the two expressions equivalent: (33)x=324?(1 point)
Responses
8
8
27
27
21
21
15
Responses
8
8
27
27
21
21
15
1 answer