Question

Given: $(-4{)}^5÷(-4{)}^8$ = $-\frac{1}{4^m}$. The value of $m$ is

Answer 1

$(-4{)}^5÷(-4{)}^8$

$=\frac{(-4{)}^5}{(-4{)}^8}$

$=\frac{1}{(-4{)}^{8-5}}$

$=\frac{1}{(-4{)}^3}$
$=\frac{1}{(-1{)}^3(4{)}^3}$
$=\frac{1}{-1\times 4^3}$
$=-\frac{1}{4^3}$