Question

simplify.
$(v^{5})^{-4}$
write your answer without using negative exponents.

Explanation:

Step1: Apply power of a power rule

When raising a power to a power, we multiply the exponents. The formula for \((a^m)^n\) is \(a^{m\times n}\). So for \((v^{5})^{-4}\), we multiply \(5\) and \(-4\).
\((v^{5})^{-4}=v^{5\times(-4)}\)

Step2: Calculate the exponent

Calculate \(5\times(-4)\) which equals \(-20\), so we have \(v^{-20}\).

Step3: Rewrite without negative exponent

A negative exponent \(a^{-n}\) can be rewritten as \(\frac{1}{a^{n}}\). So \(v^{-20}=\frac{1}{v^{20}}\)

Answer:

\(\frac{1}{v^{20}}\)