Question

which expression is equivalent to the given expression? (2w^{-2})^{3}(8w^{6})
a. 48
b. 64
c. \frac{64}{w^{2}}
d. \frac{48}{w^{2}}

Explanation:

Step1: Expand \((2w^{-2})^{3}\)

Use the power - of - a - product rule \((ab)^n=a^n b^n\) and power - of - a - power rule \((a^m)^n=a^{mn}\). So \((2w^{-2})^{3}=2^{3}\times(w^{-2})^{3}=8w^{-6}\).

Step2: Multiply by \(8w^{6}\)

\((8w^{-6})(8w^{6})\). Use the product rule \(a^m\times a^n=a^{m + n}\), so \(8\times8\times w^{-6+6}\).
\(64\times w^{0}\). Since \(w^{0}=1\) (for \(w
eq0\)), the result is \(64\).

Answer:

B. 64