Question

simplify.
$(x^{-7})^5$
write your answer without using negative exponents.

Explanation:

Step1: Apply power of a power rule

To simplify \((x^{-7})^5\), we use the power of a power rule, which states that \((a^m)^n = a^{m \times n}\). Here, \(a = x\), \(m = -7\), and \(n = 5\). So we multiply the exponents: \(-7\times5=-35\). Thus, \((x^{-7})^5 = x^{-35}\).

Step2: Convert negative exponent to positive

A negative exponent rule states that \(a^{-n}=\frac{1}{a^n}\) (where \(a
eq0\) and \(n\) is a positive integer). So for \(x^{-35}\), we can rewrite it as \(\frac{1}{x^{35}}\) to eliminate the negative exponent.

Answer:

\(\frac{1}{x^{35}}\)