Question

simplify.
$(w^{4})^{-4}$
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 \(a^{m\times n}\). For \((w^{4})^{-4}\), we multiply the exponents \(4\) and \(-4\).
\((w^{4})^{-4}=w^{4\times(-4)}\)

Step2: Calculate the exponent

Calculate \(4\times(-4)\), which equals \(-16\). So we have \(w^{-16}\).

Step3: Convert negative exponent to positive

A negative exponent \(a^{-n}\) can be rewritten as \(\frac{1}{a^{n}}\) (where \(a
eq0\)). So \(w^{-16}=\frac{1}{w^{16}}\).

Answer:

\(\frac{1}{w^{16}}\)