Question

rewrite the expression without using a negative exponent.
\\(\frac{1}{3z^{-5}}\\)
simplify your answer as much as possible.

Explanation:

Step1: Recall the negative exponent rule

The rule for negative exponents is \(a^{-n}=\frac{1}{a^{n}}\) (or \(\frac{1}{a^{-n}} = a^{n}\) when the negative exponent is in the denominator). We have the expression \(\frac{1}{3z^{-5}}\).

Step2: Apply the negative exponent rule to \(z^{-5}\)

Using the rule \(\frac{1}{a^{-n}}=a^{n}\), here \(a = z\) and \(n = 5\), so \(\frac{1}{z^{-5}}=z^{5}\). Then the expression \(\frac{1}{3z^{-5}}\) becomes \(\frac{z^{5}}{3}\) (since we have \(\frac{1}{3}\times z^{5}\)).

Answer:

\(\frac{z^{5}}{3}\)