What is the value of \(9^{\frac{3}{2}}\)?

C. 27

Explanation

Rewrite the exponent \(\frac{3}{2}\) as \(\frac{1}{2} \times 3\) to get \(9^{\left(\frac{1}{2} \times 3\right)}\). Multiplication within the exponent is equivalent to raising to an exponent, so \(9^{\left(\frac{1}{2} \times 3\right)}=\left(9^{\frac{1}{2}}\right)^{3}\). Since \(9^{\frac{1}{2}}=\sqrt{9}=3,\left(9^{\frac{1}{2}}\right)^{2}=3^{3}=27\)

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