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Use the Power Rule of Exponents to simplify the expression (6^2)^4.Question
Use the Power Rule of Exponents to simplify the expression (62)4.(
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bot that is incorrect
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Use the Power Rule of Exponents to simplify the expression (734)5
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Use the Power Rule of Exponents to simplify the expression (788)6
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Use the Power Rule of Exponents to create a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12).
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What exponent would make the two expressions equivalent: (16x)6=(1618)
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bot that is wrong
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that is incorrect
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BOT THAT IS INCORRECT THE QUESTION IS
What exponent would make the two expressions equivalent: (16^x)^6=(16^18)
What exponent would make the two expressions equivalent: (16^x)^6=(16^18)
Answered by
unkownuser
Use the Power Rule of Exponents to simplify the expression (6^2)^4.
Answered by
GPT 3.5
We can use the power rule of exponents to simplify the expression (62)4.
The power rule of exponents states that when we have a base raised to an exponent, and then that whole expression is raised to another exponent, we can multiply the exponents.
In this case, we have (62)4. Since the base is a number, 6, we can rewrite this expression as (62)4 = 64.
Therefore, the expression (62)4 simplifies to 64.
The power rule of exponents states that when we have a base raised to an exponent, and then that whole expression is raised to another exponent, we can multiply the exponents.
In this case, we have (62)4. Since the base is a number, 6, we can rewrite this expression as (62)4 = 64.
Therefore, the expression (62)4 simplifies to 64.
Answered by
GPT 3.5
Apologies for the incorrect response. Let's try again:
To simplify the expression (62)4 using the power rule of exponents, we multiply the exponents. In this case, we have the base 6 raised to the exponent 2, and then that whole expression raised to the exponent 4.
Using the power rule, we multiply the exponents:
(62)4 = 6(2*4) = 6^8
Therefore, the expression (62)4 simplifies to 6^8.
To simplify the expression (62)4 using the power rule of exponents, we multiply the exponents. In this case, we have the base 6 raised to the exponent 2, and then that whole expression raised to the exponent 4.
Using the power rule, we multiply the exponents:
(62)4 = 6(2*4) = 6^8
Therefore, the expression (62)4 simplifies to 6^8.
Answered by
GPT 3.5
To simplify the expression (734)5 using the Power Rule of Exponents, we can apply the rule which states that when a base is raised to an exponent, and then that expression is raised to another exponent, we multiply the exponents.
In this case, we have the base 734 raised to the exponent 5. Using the power rule, we can multiply the exponents:
(734)5 = 73(4*5) = 73^20
Therefore, the expression (734)5 simplifies to 73^20.
In this case, we have the base 734 raised to the exponent 5. Using the power rule, we can multiply the exponents:
(734)5 = 73(4*5) = 73^20
Therefore, the expression (734)5 simplifies to 73^20.
Answered by
GPT 3.5
To simplify the expression (788)6 using the Power Rule of Exponents, we can apply the rule which states that when a base is raised to an exponent, and then that expression is raised to another exponent, we multiply the exponents.
In this case, we have the base 788 raised to the exponent 6. Using the power rule, we can multiply the exponents:
(788)6 = 78(8*6) = 78^48
Therefore, the expression (788)6 simplifies to 78^48.
In this case, we have the base 788 raised to the exponent 6. Using the power rule, we can multiply the exponents:
(788)6 = 78(8*6) = 78^48
Therefore, the expression (788)6 simplifies to 78^48.
Answered by
GPT 3.5
To create a simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12) using the Power Rule of Exponents, we can simplify each factor individually, and then multiply them together.
First, we can simplify (12⋅12⋅12) to 12^3, using the rule that states when a number is raised to an exponent, it can be simplified by multiplying the number by itself the number of times indicated by the exponent:
(12⋅12⋅12) = 12^3
Next, we can apply the Power Rule of Exponents to simplify (12^3)⋅(12^3):
(12^3)⋅(12^3) = 12^(3+3) = 12^6
Therefore, the simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12) using the Power Rule of Exponents is 12^6.
First, we can simplify (12⋅12⋅12) to 12^3, using the rule that states when a number is raised to an exponent, it can be simplified by multiplying the number by itself the number of times indicated by the exponent:
(12⋅12⋅12) = 12^3
Next, we can apply the Power Rule of Exponents to simplify (12^3)⋅(12^3):
(12^3)⋅(12^3) = 12^(3+3) = 12^6
Therefore, the simplified equivalent expression of (12⋅12⋅12)⋅(12⋅12⋅12) using the Power Rule of Exponents is 12^6.
Answered by
GPT 3.5
To find the exponent that would make the two expressions equivalent, we need to equate the bases and set the exponents equal to each other.
We have (16x)6 = (16^18).
Comparing the bases, we see that 16^6 = 16^18.
Therefore, the exponent that would make the two expressions equivalent is 6.
We have (16x)6 = (16^18).
Comparing the bases, we see that 16^6 = 16^18.
Therefore, the exponent that would make the two expressions equivalent is 6.
Answered by
GPT 3.5
Apologies for the incorrect response. Let's correct it:
To find the exponent that would make the two expressions equivalent, we need to equate the bases and set the exponents equal to each other.
We have (16x)6 = (16^18).
Comparing the bases, we see that 16^1 = 16^18.
Therefore, the exponent that would make the two expressions equivalent is 1.
To find the exponent that would make the two expressions equivalent, we need to equate the bases and set the exponents equal to each other.
We have (16x)6 = (16^18).
Comparing the bases, we see that 16^1 = 16^18.
Therefore, the exponent that would make the two expressions equivalent is 1.
Answered by
GPT 3.5
Apologies for the mistake. Let's try again:
To find the exponent that would make the two expressions equivalent, we need to equate the bases and set the exponents equal to each other.
We have (16x)6 = (16^18).
Comparing the bases, we see that 16 = 16^18.
To determine the exponent that would make the two expressions equivalent, we need to solve for x in the equation 16 = 16^x.
Taking the logarithm of both sides of the equation, we have log(16) = x * log(16).
Since log(16) is nonzero, we can divide both sides of the equation by log(16) to isolate x:
log(16) / log(16) = x.
Simplifying, we find that x = 1.
Therefore, the exponent that would make the two expressions equivalent is 1.
To find the exponent that would make the two expressions equivalent, we need to equate the bases and set the exponents equal to each other.
We have (16x)6 = (16^18).
Comparing the bases, we see that 16 = 16^18.
To determine the exponent that would make the two expressions equivalent, we need to solve for x in the equation 16 = 16^x.
Taking the logarithm of both sides of the equation, we have log(16) = x * log(16).
Since log(16) is nonzero, we can divide both sides of the equation by log(16) to isolate x:
log(16) / log(16) = x.
Simplifying, we find that x = 1.
Therefore, the exponent that would make the two expressions equivalent is 1.
Answered by
GPT 3.5
Apologies for the misunderstanding.
To find the exponent that would make the two expressions equivalent, we can use the power rule of exponents and equate the exponents.
We have (16^x)^6 = 16^18.
Using the power rule, we multiply the exponents:
16^(6x) = 16^18.
To make the two expressions equivalent, we set the exponents equal to each other:
6x = 18.
Dividing both sides of the equation by 6, we find:
x = 3.
Therefore, the exponent that would make the two expressions equivalent is 3.
To find the exponent that would make the two expressions equivalent, we can use the power rule of exponents and equate the exponents.
We have (16^x)^6 = 16^18.
Using the power rule, we multiply the exponents:
16^(6x) = 16^18.
To make the two expressions equivalent, we set the exponents equal to each other:
6x = 18.
Dividing both sides of the equation by 6, we find:
x = 3.
Therefore, the exponent that would make the two expressions equivalent is 3.
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