Question

Which expression is equivalent to 4^ 5x4^ -7÷4 ^-2?

Answer 1

Answer:

4^0

Step-by-step explanation:

it equals 1

Answer 2

$\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 4^5\cdot 4^{-7}\div 4^{-2}\implies \cfrac{4^5\cdot 4^{-7}}{4^{-2}}\implies \cfrac{4^{5-7}}{4^{-2}}\implies \cfrac{4^{-2}}{4^{-2}}\implies 4^{-2}\cdot 4^2 \\\\\\ 4^{-2+2}\implies \boxed{4^0}\implies 1$