QuestionCalculate $\left(\frac{9 n^{2}}{8}\right)^{3}$ and choose from: A) $\frac{9 n^{6}}{8}$ , B) $\frac{729 n^{6}}{8}$ , C) $\frac{729 n^{6}}{512}$ , D) $\frac{729 n^{5}}{512}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the expression $\left(\frac{9 n^{}}{8}\right)^{3}$ and we need to simplify it. . We are given four options and we need to select the correct one.

STEP 2

We need to apply the power of a power rule in exponents. The power of a power rule states that $(a^m)^n = a^{m \times n}$ . $\left(\frac{9 n^{2}}{8}\right)^{} = \left(9^{} \times (n^{2})^{}\right) /8^{}$

STEP 3

Calculate the value of $9^{3}$ , $(n^{2})^{3}$ and $8^{3}$ .
$9^{3} =729$ $(n^{2})^{3} = n^{6}$ $8^{3} =512$

STEP 4

Substitute the values back into the equation.
$\left(\frac{9 n^{2}}{8}\right)^{3} = \frac{729 n^{6}}{512}$ So, the correct answer is $\frac{729 n^{6}}{512}$ .

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