Question

which statement best describes the meaning of 9^{\frac{3}{2}}?

Explanation:

Step1: Recall exponent - fraction rule

The general rule for a fractional exponent $a^{\frac{m}{n}}$ is $\sqrt[n]{a^{m}}$. In the case of $9^{\frac{3}{2}}$, $a = 9$, $m = 3$, and $n=2$.

Step2: Rewrite using the rule

$9^{\frac{3}{2}}=\sqrt{9^{3}}$. First, calculate $9^{3}=9\times9\times9 = 729$. Then $\sqrt{9^{3}}=\sqrt{729}$. Also, we can rewrite $9^{\frac{3}{2}}$ as $(\sqrt{9})^{3}$. Since $\sqrt{9}=3$, then $(\sqrt{9})^{3}=3^{3}=27$.

Answer:

$9^{\frac{3}{2}}$ is equivalent to the square - root of $9$ cubed or the cube of the square - root of $9$, and its value is 27.