Question

Which expressions are equivalent to this exponential expression?

Answer 1

Remember that when the exponents look like this (5^2)^-3, you multiply the exponents together

when it looks like this:
5^3 x 5^2 you add the exponents
so my example would equal 5^5

also remember that you can’t have negative exponents

To solve your problem:
1. multiply the exponents here: (5^2)^-3

2. add the exponents in the next step when you multiply by the 5^4

3. now, you should get a negative exponent on the top, and you already have one on the bottom. to get rid of these negative exponents, move the one in the denominator to the numerator and vice versa

so when you move the 5^-4 in the denominator to the numerator, it becomes 5^4

4. now, you simplify. you can either subtract the exponents and do it that way, or you can solve the exponents and then divide. either way will work, although the first is easier