Determine if each pair of expressions is equivalent. Explain your reasoning.

Question

a: 1/3^2 and 3^-2
b: 1/4^-3 and 4^-3

My answer: a: 1/3^2 = 1/9 and 3^-2 = 0.111111111; these pair of expressions are not equivalent.
b: 1/4^-3 = 64 and 4^-3 = 0.015625; these pair of expressions are not equivalent.

Need help!

Answer 1

Rule for negative exponents:
x^-a = 1/x^a
so: 3^-2 = 1/3^2 , YES
4^-3 = 1/4^3, in the question the result said: 1/4^-3 = 4^-3 , so NO

the last one should have been obvious even without knowing the rule.

btw, 1/9 = .111111.....