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Step-by-step explanation:

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Step-by-step explanation:

A. when you multiply exponents with a common base you keep the base and add the exponents. In this case you would keep the 6 and add the -5 and 2 so the answer would be:

6^-3 which is not equivalent

B. You can distribute the exponent in to the parenthesis.

(1^5)/(6^2)^5

when you have an exponent to an exponent you mutliply. so the answer would be:

1^5/6^10

1^5 is always going to be 1 so you actually have:

1/6^10

when the exponent is on the bottom you can bring it to the top by making it negative, so the final answer for B is:

6^-10 which is equivalent

C. Same rules as B, multiply an exponent to an exponent.

6^(-5*2) = 6^-10 which is equivalent

D. When you are dividing exponents with a common base you subtract the top and bottom exponents. So in this case you have:

6^(-3-7) = 6^-10 which is equivalent

E. Using the rules from eariler the numerator can be simplified by adding the exponents.

6^5 * 6^-3 = 6^(5-3) = 6^2

which leaves you with:

6^2/6^-8

From there you can either bring the 6^-8 to the numberator to make it positive which simplifies to:

6^2 * 6^8 = 6^(2+8) = 6^10 which is not equivalent

or you can subtract the top and bottom exponents:

6^2/6^-8 = 6^(2-(-8))

the double negative cancels to a positive and you getL

6^(2+8) = 6^10 which is not equivalent

so B, C, and D are equal to 6^-10