Question

which of the following is equivalent to $16^{\frac{3}{4}}$? options: 64, 8, 6, 12

Explanation:

Step1: Recall exponent rule

The expression is \(16^{\frac{3}{2}}\). Using the exponent rule \(a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m\), we can rewrite it as \((\sqrt{16})^3\).

Step2: Calculate square root

\(\sqrt{16} = 4\), so now we have \(4^3\).

Step3: Calculate the power

\(4^3=4\times4\times4 = 64\).

Answer:

64 (the option with the number 64)