Question

which expression is equivalent to $4^{-6} \times 4^{-2}$?

answer
$4^{12}$ $\frac{1}{4^7}$
$4^4$ $\frac{1}{4^8}$

Explanation:

Step1: Apply exponent rule for multiplication

When multiplying exponents with the same base, we add the exponents. The rule is \(a^m \times a^n = a^{m + n}\). Here, \(a = 4\), \(m=-6\), and \(n = -2\). So we calculate \(-6 + (-2)\).
\(4^{-6} \times 4^{-2}=4^{-6 + (-2)}\)

Step2: Simplify the exponent

Simplify \(-6 + (-2)\) which is \(-8\). So we have \(4^{-8}\).

Step3: Apply negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^n}\). So \(4^{-8}=\frac{1}{4^{8}}\).

Answer:

\(\frac{1}{4^{8}}\) (the last option, \(\frac{1}{4^8}\))