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Use the Power Rule of Exponents to simplify the expression (62)4.(
Bot GPT 3.5
answered
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.
anonymous
answered
bot that is incorrect
Bot GPT 3.5
answered
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.
anonymous
answered
Use the Power Rule of Exponents to simplify the expression (734)5
Bot GPT 3.5
answered
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.
anonymous
answered
Use the Power Rule of Exponents to simplify the expression (788)6
Bot GPT 3.5
answered
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.
anonymous
answered
Use the Power Rule of Exponents to create a simplified equivalent expression of (12â‹…12â‹…12)â‹…(12â‹…12â‹…12).
Bot GPT 3.5
answered
To create a simplified equivalent expression of (12â‹…12â‹…12)â‹…(12â‹…12â‹…12) using the Power Rule of Exponents, we can simplify each factor individually, and then multiply them together.
First, we can simplify (12â‹…12â‹…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:
(12â‹…12â‹…12) = 12^3
Next, we can apply the Power Rule of Exponents to simplify (12^3)â‹…(12^3):
(12^3)â‹…(12^3) = 12^(3+3) = 12^6
Therefore, the simplified equivalent expression of (12â‹…12â‹…12)â‹…(12â‹…12â‹…12) using the Power Rule of Exponents is 12^6.
anonymous
answered
What exponent would make the two expressions equivalent: (16x)6=(1618)
Bot GPT 3.5
answered
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.
anonymous
answered
bot that is wrong
Bot GPT 3.5
answered
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.
anonymous
answered
that is incorrect
Bot GPT 3.5
answered
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.
anonymous
answered
BOT THAT IS INCORRECT THE QUESTION IS
What exponent would make the two expressions equivalent: (16^x)^6=(16^18)
Bot GPT 3.5
answered
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.
unkownuser
answered