It seems like there might be a mistake in the question. The Product Rule of Exponents states that when multiplying two exponential expressions with the same base, you add the exponents. However, the given expression has two different bases, 5 and 10.
To simplify the given expression, you would keep each base separate and calculate the exponents separately.
510 * 55 = (5^10) * (5^5)
Using the Product Rule of Exponents, you add the exponents:
5^10 * 5^5 = 5^(10+5) = 5^15
Therefore, the simplified expression is 5^15.
Use the Product Rule of Exponents to simplify 510⋅55(1 point)
Responses
550
5 superscript 50 baseline
2515
25 superscript 15 baseline
2550
25 superscript 50 baseline
515
55 answers
What is the missing exponent in the following equation?
h450h? = h215
h450h? = h215
The missing exponent can be determined using the Product Rule of Exponents. According to the Product Rule, when multiplying two exponential expressions with the same base, the exponents are added together.
In the given equation, h450h? = h215, we have the bases on both sides of the equation as h.
Using the Product Rule, we can set up the equation:
( h^4 )^50 * h^? = ( h^2 )^15
To simplify this equation, we multiply the exponents on each side:
h^(4*50) * h^? = h^(2*15)
h^200 * h^? = h^30
Now, we can use the rule of combining exponentials with the same base:
h^(200 + ?) = h^30
Since the bases on both sides of the equation are the same (h), the exponents must be equal:
200 + ? = 30
Solving for ?, we subtract 200 from both sides:
? = 30 - 200
? = -170
Therefore, the missing exponent in the equation is -170.
In the given equation, h450h? = h215, we have the bases on both sides of the equation as h.
Using the Product Rule, we can set up the equation:
( h^4 )^50 * h^? = ( h^2 )^15
To simplify this equation, we multiply the exponents on each side:
h^(4*50) * h^? = h^(2*15)
h^200 * h^? = h^30
Now, we can use the rule of combining exponentials with the same base:
h^(200 + ?) = h^30
Since the bases on both sides of the equation are the same (h), the exponents must be equal:
200 + ? = 30
Solving for ?, we subtract 200 from both sides:
? = 30 - 200
? = -170
Therefore, the missing exponent in the equation is -170.
you sure
Apologies for the mistake in the previous response. Let's re-evaluate the given equation:
h^450 * h^? = h^215
According to the Product Rule of Exponents, when we multiply two exponential expressions with the same base, we add the exponents.
Therefore, for the left side of the equation:
h^450 * h^? = h^(450 + ?)
The right side of the equation is already expressed as h^215.
So, we can rewrite the equation as:
h^(450 + ?) = h^215
For the equation to hold true, the exponents on both sides must be equal:
450 + ? = 215
To solve for ?, we subtract 450 from both sides:
? = 215 - 450
? = -235
Therefore, the missing exponent in the equation is -235.
h^450 * h^? = h^215
According to the Product Rule of Exponents, when we multiply two exponential expressions with the same base, we add the exponents.
Therefore, for the left side of the equation:
h^450 * h^? = h^(450 + ?)
The right side of the equation is already expressed as h^215.
So, we can rewrite the equation as:
h^(450 + ?) = h^215
For the equation to hold true, the exponents on both sides must be equal:
450 + ? = 215
To solve for ?, we subtract 450 from both sides:
? = 215 - 450
? = -235
Therefore, the missing exponent in the equation is -235.
Simplify 1287÷1225.
To simplify 1287 ÷ 1225, we divide the numerator (1287) by the denominator (1225).
1287 ÷ 1225 = 1.0514285714
So, the simplified form of 1287 ÷ 1225 is approximately 1.0514285714.
1287 ÷ 1225 = 1.0514285714
So, the simplified form of 1287 ÷ 1225 is approximately 1.0514285714.
answer
1287 ÷ 1225 simplifies to 1.052
What is the value of 6.9−20?(1 point)
Responses
6.9
6.9
7.9
7.9
5.9
5.9
4.9
Responses
6.9
6.9
7.9
7.9
5.9
5.9
4.9
The value of 6.9 - 20 is -13.1
the answer
Apologies for the mistake in the previous response.
The value of 6.9 - 20 is -13.1.
The value of 6.9 - 20 is -13.1.
it is not on the responses
Apologies for the confusion. The correct answer is not among the provided responses.
The correct answer for 6.9 - 20 is -13.1.
The correct answer for 6.9 - 20 is -13.1.
What is the value of 6.9−2^0?(1 point)
The value of 2^0 is equal to 1. Therefore, the value of 6.9 - 2^0 is:
6.9 - 1 = 5.9
6.9 - 1 = 5.9
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)0+32(8−270).(2 points)
9⋅(−33)0+32(8−270) =
⋅
+32(
–
)
9⋅(−33)0+32(8−270) =
⋅
+32(
–
)
To apply the Zero Power Rule, any non-zero number raised to the power of zero is equal to 1. This means that (-33)^0 is equal to 1.
Using this rule, the expression 9⋅(−33)0+32(8−270) can be simplified to:
9⋅1 + 32(8−270)
Simplifying the expression further:
9 + 32(8−270)
Therefore, the equivalent expression to 9⋅(−33)0+32(8−270) is:
9 + 32(8−270)
Using this rule, the expression 9⋅(−33)0+32(8−270) can be simplified to:
9⋅1 + 32(8−270)
Simplifying the expression further:
9 + 32(8−270)
Therefore, the equivalent expression to 9⋅(−33)0+32(8−270) is:
9 + 32(8−270)
what?
Apologies for any confusion caused.
To simplify the given expression using the Zero Power Rule, we need to evaluate any expressions raised to the power of 0 as 1.
In the given expression, we have (-33)^0. According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1. Therefore, (-33)^0 simplifies to 1.
Using this rule, the original expression 9⋅(-33)^0 + 32(8 − 270) simplifies to:
9⋅1 + 32(8 − 270)
Now, we simplify the expression further by performing the operations inside the parentheses:
9 + 32(-262)
Finally, we can evaluate the multiplication:
9 - 8384
Therefore, the simplified form of the given expression is:
-8375
To simplify the given expression using the Zero Power Rule, we need to evaluate any expressions raised to the power of 0 as 1.
In the given expression, we have (-33)^0. According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1. Therefore, (-33)^0 simplifies to 1.
Using this rule, the original expression 9⋅(-33)^0 + 32(8 − 270) simplifies to:
9⋅1 + 32(8 − 270)
Now, we simplify the expression further by performing the operations inside the parentheses:
9 + 32(-262)
Finally, we can evaluate the multiplication:
9 - 8384
Therefore, the simplified form of the given expression is:
-8375
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)0+32(8−270).(2 points)
To apply the Zero Power Rule to the given expression, we need to simplify any exponent of 0 to 1.
In this case, (-33)^0 becomes 1.
Using the Zero Power Rule, the expression:
9⋅(−33)0+32(8−270)
simplifies to:
9⋅1 + 32(8−270)
Simplifying the parentheses:
9 + 32(-262)
Lastly, we evaluate the multiplication:
9 - 8384
Therefore, the equivalent expression using the Zero Power Rule is:
-8375
In this case, (-33)^0 becomes 1.
Using the Zero Power Rule, the expression:
9⋅(−33)0+32(8−270)
simplifies to:
9⋅1 + 32(8−270)
Simplifying the parentheses:
9 + 32(-262)
Lastly, we evaluate the multiplication:
9 - 8384
Therefore, the equivalent expression using the Zero Power Rule is:
-8375
Solve the expression 15⋅805+4(70−6).(1 point)
15⋅805+4(70−6)=
15⋅805+4(70−6)=
To solve the expression 15⋅805+4(70−6), we will perform the operations in the parentheses first and then continue with the rest of the expression.
Inside the parentheses:
70 - 6 = 64
Now, we substitute this value back into the expression:
15⋅805 + 4(64)
Next, we evaluate the multiplication within the parentheses:
4 * 64 = 256
Now, we substitute this value back into the expression:
15⋅805 + 256
Finally, we evaluate the remaining multiplication:
15 * 805 = 12,075
Now, we substitute this value back into the expression:
12,075 + 256
And finally, we add the two values together:
12,075 + 256 = 12,331
Therefore, the simplified value of the expression 15⋅805+4(70−6) is 12,331.
Inside the parentheses:
70 - 6 = 64
Now, we substitute this value back into the expression:
15⋅805 + 4(64)
Next, we evaluate the multiplication within the parentheses:
4 * 64 = 256
Now, we substitute this value back into the expression:
15⋅805 + 256
Finally, we evaluate the remaining multiplication:
15 * 805 = 12,075
Now, we substitute this value back into the expression:
12,075 + 256
And finally, we add the two values together:
12,075 + 256 = 12,331
Therefore, the simplified value of the expression 15⋅805+4(70−6) is 12,331.
what
Apologies for the confusion caused by the incorrect response. Let's recalculate the expression correctly.
To solve the expression 15⋅805+4(70−6), we will first simplify what is inside the parentheses:
70 - 6 = 64
Now, we substitute this value back into the expression:
15⋅805 + 4(64)
Next, we evaluate the multiplication within the parentheses:
4 * 64 = 256
Now, we substitute this value back into the expression:
15⋅805 + 256
Finally, we evaluate the remaining multiplication:
15 * 805 = 12,075
Now, we substitute this value back into the expression:
12,075 + 256
And finally, we add the two values together:
12,075 + 256 = 12,331
Therefore, the simplified value of the expression 15⋅805+4(70−6) is 12,331.
To solve the expression 15⋅805+4(70−6), we will first simplify what is inside the parentheses:
70 - 6 = 64
Now, we substitute this value back into the expression:
15⋅805 + 4(64)
Next, we evaluate the multiplication within the parentheses:
4 * 64 = 256
Now, we substitute this value back into the expression:
15⋅805 + 256
Finally, we evaluate the remaining multiplication:
15 * 805 = 12,075
Now, we substitute this value back into the expression:
12,075 + 256
And finally, we add the two values together:
12,075 + 256 = 12,331
Therefore, the simplified value of the expression 15⋅805+4(70−6) is 12,331.
Use the Power Rule of Exponents to simplify (10^3)^6.
To simplify (10^3)^6 using the Power Rule of Exponents, we multiply the exponents:
(10^3)^6 = 10^(3*6) = 10^18
Therefore, the simplified form of (10^3)^6 is 10^18.
(10^3)^6 = 10^(3*6) = 10^18
Therefore, the simplified form of (10^3)^6 is 10^18.
If the expression 7^15 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression?(1 point)
Responses
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis
(718)3
left parenthesis 7 superscript 18 baseline right parenthesis cubed
(710)5
left parenthesis 7 superscript 10 baseline right parenthesis superscript 5 baseline
(7⋅7⋅7⋅7⋅7)10
left parenthesis 7 times 7 times 7 times 7 times 7 right parenthesis superscript 10 baseline
Responses
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis times left parenthesis 7 times 7 times 7 right parenthesis
(718)3
left parenthesis 7 superscript 18 baseline right parenthesis cubed
(710)5
left parenthesis 7 superscript 10 baseline right parenthesis superscript 5 baseline
(7⋅7⋅7⋅7⋅7)10
left parenthesis 7 times 7 times 7 times 7 times 7 right parenthesis superscript 10 baseline
If the expression 7^15 is simplified using the Power Rule of Exponents, an expanded equivalent expression would be:
(7⋅7⋅7⋅7⋅7)⋅(7⋅7⋅7⋅7⋅7)
This is because 7 raised to the power of 15 means multiplying 7 by itself 15 times. Using the expanded form, we can see that 7 is multiplied by itself five times, then that product is multiplied by itself another five times.
Therefore, the expanded equivalent expression is (7⋅7⋅7⋅7⋅7)⋅(7⋅7⋅7⋅7⋅7).
(7⋅7⋅7⋅7⋅7)⋅(7⋅7⋅7⋅7⋅7)
This is because 7 raised to the power of 15 means multiplying 7 by itself 15 times. Using the expanded form, we can see that 7 is multiplied by itself five times, then that product is multiplied by itself another five times.
Therefore, the expanded equivalent expression is (7⋅7⋅7⋅7⋅7)⋅(7⋅7⋅7⋅7⋅7).
huh
Apologies for the confusion caused by the previous response. Let's re-evaluate the given expression.
If the expression 7^15 (7 raised to the power of 15) is simplified using the Power Rule of Exponents, the expanded equivalent expression would be:
(7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7)
This is because simplifying 7^15 means multiplying 7 by itself 15 times, which can be represented as multiplying 7 fifteen times using multiplication signs (⋅).
Therefore, the expanded equivalent expression of 7^15 is (7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7).
If the expression 7^15 (7 raised to the power of 15) is simplified using the Power Rule of Exponents, the expanded equivalent expression would be:
(7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7)
This is because simplifying 7^15 means multiplying 7 by itself 15 times, which can be represented as multiplying 7 fifteen times using multiplication signs (⋅).
Therefore, the expanded equivalent expression of 7^15 is (7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7⋅7).
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9.(1 point)
To create a simplified equivalent expression for (19^4)^9 using the Power Rule of Exponents, we multiply the exponents:
(19^4)^9 = 19^(4*9) = 19^36
Therefore, the simplified equivalent expression for (19^4)^9 is 19^36.
(19^4)^9 = 19^(4*9) = 19^36
Therefore, the simplified equivalent expression for (19^4)^9 is 19^36.
Apply the Property of Negative Integer Exponents to solve 7−3. The answer should not contain any exponent expression or decimals.(1 point)
7−3=
7−3=
To apply the Property of Negative Integer Exponents to solve 7^(-3), we can rewrite it as the reciprocal of 7^3:
7^(-3) = 1/(7^3)
Using the definition that any number raised to the power of -d is equal to 1 divided by that number raised to the power of d, we can further simplify:
1/(7^3) = 1/343
Therefore, the simplified form of 7^(-3) is 1/343.
7^(-3) = 1/(7^3)
Using the definition that any number raised to the power of -d is equal to 1 divided by that number raised to the power of d, we can further simplify:
1/(7^3) = 1/343
Therefore, the simplified form of 7^(-3) is 1/343.
huh?
Apologies for the confusion caused by the previous response. Let's re-evaluate the given expression using the Property of Negative Integer Exponents.
The Property of Negative Integer Exponents states that a number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent.
For the expression 7^(-3):
7^(-3) = 1/(7^3)
Therefore, the simplified form of 7^(-3) is 1/7^3.
Simplifying further:
7^3 = 7 * 7 * 7 = 343
So, the simplified form of 7^(-3) is 1/343.
The Property of Negative Integer Exponents states that a number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent.
For the expression 7^(-3):
7^(-3) = 1/(7^3)
Therefore, the simplified form of 7^(-3) is 1/7^3.
Simplifying further:
7^3 = 7 * 7 * 7 = 343
So, the simplified form of 7^(-3) is 1/343.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3−178−14 with positive exponents only.(1 point)
3−178−14=
3−178−14=
To apply the Property of Negative Integer Exponents and generate an expression equivalent to 3^(-17) * 8^(-14) with positive exponents only, we can rewrite each term with positive exponents.
First, let's rewrite 3^(-17):
3^(-17) = 1/(3^17)
Next, let's rewrite 8^(-14):
8^(-14) = 1/(8^14)
Therefore, the expression 3^(-17) * 8^(-14) with positive exponents only is:
1/(3^17) * 1/(8^14)
Hence, the simplified expression with positive exponents only is 1/(3^17 * 8^14).
First, let's rewrite 3^(-17):
3^(-17) = 1/(3^17)
Next, let's rewrite 8^(-14):
8^(-14) = 1/(8^14)
Therefore, the expression 3^(-17) * 8^(-14) with positive exponents only is:
1/(3^17) * 1/(8^14)
Hence, the simplified expression with positive exponents only is 1/(3^17 * 8^14).
Apply the Properties of Integer Exponents to generate equivalent expressions to (7−3)7 ⋅ 7206−2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction.(1 point)
(7−3)7 ⋅ 7206−2=
(7−3)7 ⋅ 7206−2=
To apply the Properties of Integer Exponents and generate equivalent expressions with only positive exponents, we can simplify each term individually:
(7^-3)7 = (1/7^3) * 7 = 1/7^2
7206^-2 = 1/7206^2
Now we can substitute these simplified forms back into the original expression:
(1/7^2) * (1/7206^2)
To multiply these expressions together, we can combine the numerators and denominators:
1 * 1 / (7^2 * 7206^2)
Simplifying further:
1 / (49 * 52059916)
Now let's evaluate the denominator:
49 * 52059916 = 2549815184
Finally, the simplified expression is:
1 / 2549815184
Therefore, the value of the expression (7^-3)7 ⋅ 7206^-2, with only positive exponents, is 1/2549815184 expressed as an improper fraction.
(7^-3)7 = (1/7^3) * 7 = 1/7^2
7206^-2 = 1/7206^2
Now we can substitute these simplified forms back into the original expression:
(1/7^2) * (1/7206^2)
To multiply these expressions together, we can combine the numerators and denominators:
1 * 1 / (7^2 * 7206^2)
Simplifying further:
1 / (49 * 52059916)
Now let's evaluate the denominator:
49 * 52059916 = 2549815184
Finally, the simplified expression is:
1 / 2549815184
Therefore, the value of the expression (7^-3)7 ⋅ 7206^-2, with only positive exponents, is 1/2549815184 expressed as an improper fraction.
answer?
The final answer for the expression (7^-3)7 ⋅ 7206^-2, with only positive exponents, is 1/2549815184, expressed as an improper fraction.
Exponent Rules Unit Test
13 of 1513 of 15 Items
Question
Simplify the expression (4x^3)^2 using the properties of integer exponents.(1 point)
Responses
16x6
16 x superscript 6 baseline
4x6
4 x superscript 6 baseline
8x6
8 x superscript 6 baseline
16x5
13 of 1513 of 15 Items
Question
Simplify the expression (4x^3)^2 using the properties of integer exponents.(1 point)
Responses
16x6
16 x superscript 6 baseline
4x6
4 x superscript 6 baseline
8x6
8 x superscript 6 baseline
16x5
To simplify the expression (4x^3)^2 using the properties of integer exponents, we can apply the power rule, which states that when you raise a power to another power, you multiply the exponents.
In this case, we have:
(4x^3)^2
By applying the power rule, we multiply the exponents:
4^2 * (x^3)^2
Simplifying further:
16 * x^(3*2)
Which simplifies to:
16 * x^6
Therefore, the simplified expression is 16x^6.
In this case, we have:
(4x^3)^2
By applying the power rule, we multiply the exponents:
4^2 * (x^3)^2
Simplifying further:
16 * x^(3*2)
Which simplifies to:
16 * x^6
Therefore, the simplified expression is 16x^6.
Apply the properties of integer exponents to generate an equivalent algebraic expression to (4x4y−4)3(x7y3)2.(1 point)
Responses
64x20
Start Fraction 64 over x superscript 20 baseline End Fraction
4x2y18
Start Fraction 4 over x squared y superscript 18 baseline End Fraction
x2y1864
Start Fraction x squared y superscript 18 baseline over 64 End Fraction
64x2y18
Responses
64x20
Start Fraction 64 over x superscript 20 baseline End Fraction
4x2y18
Start Fraction 4 over x squared y superscript 18 baseline End Fraction
x2y1864
Start Fraction x squared y superscript 18 baseline over 64 End Fraction
64x2y18
To apply the properties of integer exponents and generate an equivalent algebraic expression to (4x^4y^-4)^3(x^7y^3)^2, we can simplify each term separately and then multiply them together.
Let's simplify the first term, (4x^4y^-4)^3:
(4x^4y^-4)^3 = 4^3 * (x^4)^3 * (y^-4)^3
Simplifying further:
64 * x^(4*3) * y^(-4*3)
Which simplifies to:
64 * x^12 * y^(-12)
Now let's simplify the second term, (x^7y^3)^2:
(x^7y^3)^2 = (x^7)^2
Let's simplify the first term, (4x^4y^-4)^3:
(4x^4y^-4)^3 = 4^3 * (x^4)^3 * (y^-4)^3
Simplifying further:
64 * x^(4*3) * y^(-4*3)
Which simplifies to:
64 * x^12 * y^(-12)
Now let's simplify the second term, (x^7y^3)^2:
(x^7y^3)^2 = (x^7)^2
are you sure?
are you sure?
exponents rules unit test- no bots, someone just tell em all answeers
Yeah.
bot
fr, i miss the old days of questions llc.
1 answer