Question

Does anyone know how to do this problem? If you can explain the steps as well it will be helpful. xx

Answer 1

The relevant rules of exponents are
$x^{a}\cdot x^{b}=x^{(a+b)}\\\\\left(x^{a}\right)^{b}=x^{(a\cdot b)}\\\\x^{-a}=\dfrac{1}{x^{a}}$

1. $\dfrac{\left(8^{3}\right)^{4}\cdot 8^{-9}}{8^{3}}=8^{(3\cdot 4-9-3)}=8^{0}=1$

2. $\dfrac{8^{3}\cdot 8^{4}}{\left(8^{2}\right)^{4}}=8^{(3+4-2\cdot 4)}=8^{-1}$