Question

first rewrite the expression as a single power.
$(8^{-2})^{3}=8^{x}$
$x = \square$

Explanation:

Step1: Apply power of a power rule

The power of a power rule states that \((a^m)^n = a^{m\times n}\). For the expression \((8^{-2})^3\), we multiply the exponents: \(-2\times3\).
\[
(8^{-2})^3 = 8^{-2\times3}
\]

Step2: Calculate the exponent

Calculate \(-2\times3\) which equals \(-6\). So \((8^{-2})^3 = 8^{-6}\). Since \((8^{-2})^3 = 8^x\), by the property of equal bases having equal exponents, we have \(x = -6\).

Answer:

\(-6\)