Asked by Glitchtrap

Use the Product Rule of Exponents to simplify the expression 24 ⋅22 .

Answers

Answered by GPT 3.5
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.
Answered by Glitchtrap
Question
Use the Product Rule of Exponents to simplify the expression 3
6^8 ⋅3^3 .
Answered by GPT 3.5
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.
Answered by Glitchtrap
Use the Product Rule of Exponents to simplify the expression 75 ⋅72
Answered by GPT 3.5
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.
Answered by Glitchtrap
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
Answered by GPT 3.5
The expression that is correctly developed to use the Product Rule of Exponents is 62⋅73 (6 squared times 7 cubed).
Answered by Glitchtrap
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
Answered by GPT 3.5
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).
Answered by Glitchtrap
Find the numerical equivalent of 102 ⋅103(1 point)
Responses

100,000
100,000

105
10 superscript 5 baseline

10
10

1,100
Answered by GPT 3.5
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.
Answered by Glitchtrap
Find the numerical equivalent of 25 ⋅2−2(1 point)
Responses

128
128

8
8

2
2

16
Answered by GPT 3.5
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.
Answered by Glitchtrap
Find the numerical equivalent of 49⋅4−7(1 point)
Responses

416
4 superscript 16 baseline

16
16

42
4 squared

4
Answered by GPT 3.5
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.
Answered by Glitchtrap
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
Answered by GPT 3.5
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.
Answered by Glitchtrap
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
Answered by GPT 3.5
The expression a^67b^34 cannot be simplified further or written in another form. Therefore, the simplified expression is still a^67b^34.
Answered by Glitchtrap
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
Answered by GPT 3.5
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.
Answered by Glitchtrap
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
Answered by GPT 3.5
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.
Answered by Glitchtrap
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.
Answered by GPT 3.5
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.
Answered by Glitchtrap
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)
Answered by GPT 3.5
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.
Answered by Glitchtrap
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
Answered by GPT 3.5
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.
Answered by Glitchtrap
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
Answered by GPT 3.5
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.
Answered by Glitchtrap
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
Answered by GPT 3.5
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.
Answered by Glitchtrap
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
Answered by GPT 3.5
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.
Answered by Glitchtrap
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
Answered by GPT 3.5
The expression that is correctly developed to use the Power Rule of Exponents is (7^8) ⋅ (7^10) = (7^(8+10)) = 7^18.
Answered by Glitchtrap
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
Answered by GPT 3.5
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).
Answered by Glitchtrap
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
Answered by GPT 3.5
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.
Answered by Glitchtrap
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
Answered by GPT 3.5
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).
Answered by Glitchtrap
What exponent would make the two expressions equivalent: (33)x=324?(1 point)
Responses

8
8

27
27

21
21

15

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