Question

in the following equation, what is the value of r?
$(2^{7})^{-2} = 2^{r}$
$r = \square$

Explanation:

Step1: Recall exponent rule \((a^m)^n = a^{m\times n}\)

For \((2^7)^{-2}\), apply the rule: \(m = 7\), \(n=-2\), so \((2^7)^{-2}=2^{7\times(-2)}\)

Step2: Calculate the exponent

\(7\times(-2)= - 14\), so \((2^7)^{-2}=2^{-14}\)
Since \((2^7)^{-2}=2^r\), then \(r=-14\)

Answer:

\(-14\)