Answer:
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
