Question

simplify.\\(\frac{z^{-8}}{z^{-5}}\\)write your answer with a positive exponent only.

Explanation:

Step1: Apply exponent rule for division

When dividing exponents with the same base, subtract the exponents: $\frac{a^m}{a^n} = a^{m - n}$. So for $\frac{z^{-8}}{z^{-5}}$, we have $z^{-8 - (-5)}$.

Step2: Simplify the exponent

Calculate $-8 - (-5) = -8 + 5 = -3$. So we get $z^{-3}$.

Step3: Convert to positive exponent

Using the rule $a^{-n} = \frac{1}{a^n}$, $z^{-3}$ becomes $\frac{1}{z^3}$.

Answer:

$\frac{1}{z^3}$