Question

question 20 of 25
which of the following is equal to the expression below?
$(6^{-8})^4$
a. $\frac{1}{6^{32}}$
b. $\frac{1}{6^4}$
c. $-6^{32}$
d. $-6^4$

Explanation:

Step1: Apply exponent rule

When raising a power to a power, multiply the exponents: \((a^m)^n = a^{m\times n}\). For \((6^{-8})^4\), we multiply \(-8\) and \(4\): \(-8\times4=-32\), so \((6^{-8})^4 = 6^{-32}\).

Step2: Rewrite negative exponent

A negative exponent \(a^{-n}=\frac{1}{a^n}\), so \(6^{-32}=\frac{1}{6^{32}}\).

Answer:

A. \(\frac{1}{6^{32}}\)