GRE Sample Test 4 Quantitative Reasoning 1

First, find the value of m. You are told that $3^{\mathit{m}}$ is 81. Well, 81 is 9 × 9 and 9 is $3^2$. So you have $3^2\times 3^2$ = 81 or 3 × 3 × 3 × 3 = 81. There are four factors of 3in 81, so m has the value 4. Now $4^3$ is 4 × 4 × 4 is 64. So (D) is correct. Note that (A) is a trap—that’s the value of m, not ${\mathit{m}}^3$.