Question

simplify. express your answer using positive exponents. \\(\frac{z^{-8}}{z^{-2}}\\)

Explanation:

Step1: Apply exponent rule for division

When dividing exponents with the same base, subtract the exponents: $\frac{z^m}{z^n}=z^{m - n}$. Here, $m=-8$ and $n = - 2$, so $\frac{z^{-8}}{z^{-2}}=z^{-8-(-2)}$.

Step2: Simplify the exponent

Simplify the exponent: $-8-(-2)=-8 + 2=-6$. So we have $z^{-6}$.

Step3: Convert to positive exponent

Use the rule $a^{-n}=\frac{1}{a^n}$, so $z^{-6}=\frac{1}{z^{6}}$.

Answer:

$\frac{1}{z^{6}}$