Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 27, 2023

Simplify the expression $\frac{a^{8}}{a^{-8}}$ .

STEP 1

Assumptions1. a is a non-zero real number. The rules of exponents apply

STEP 2

We can simplify the expression by using the rule of exponents that states $a^{m}/a^{n}=a^{m-n}$ .
$\frac{a^{8}}{a^{-8}} = a^{8-(-8)}$

STEP 3

implify the exponent.
$a^{8-(-8)} = a^{8+8}$

STEP 4

Calculate the exponent.
$a^{8+8} = a^{16}$ So, $\frac{a^{8}}{a^{-8}} = a^{16}$ .

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