Question

Using laws of exponents, simplify and write the answer in exponential form: $\frac{8^t}{8^2}$

Answer 1

Given $\frac{8^t}{8^2}$

Let $a=\frac{8^t}{8^2}$

using $\frac{a^m}{a^n}=a^{m-n}$

$=8^{t-2}$

$={\left(2^3\right)}^{t-2}$

using $\left(a^m\right)n=a^{mn}$

$a=2^{3t-6}$

$\frac{8^t}{8^2}=2^{3t-6}$