Question

Evaluate the expression

$\frac{8^2}{8^4}$

Answer 1

Evaluating the expression

$\frac{8^2}{8^4}$

$=8^{2-4}$ (Using exponent law $\frac{{\mathrm{a}}^{\mathrm{m}}}{{\mathrm{a}}^{\mathrm{n}}}={\mathrm{a}}^{\mathrm{m}-\mathrm{n}}$)

$=8^{-2}$

$=\frac{1}{8^2}$ (Using exponent law ${\mathrm{a}}^{-\mathrm{n}}=\frac{1}{{\mathrm{a}}^{\mathrm{n}}}$)

$=\frac{1}{8\times 8}$

$=\frac{1}{64}$

Hence, the expression is $\frac{8^2}{8^4}=\frac{1}{64}$.