Question

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

Explanation:

Step1: Recall exponent rule

For \(a^{\frac{m}{n}}\), it can be rewritten as \((a^{\frac{1}{n}})^m\) or \(\sqrt[n]{a^m}\). Here, \(a = 16\), \(m = 3\), \(n = 4\). So \(16^{\frac{3}{4}}=(16^{\frac{1}{4}})^3\).

Step2: Simplify \(16^{\frac{1}{4}}\)

Since \(2^4 = 16\), then \(16^{\frac{1}{4}}=2\).

Step3: Calculate \((16^{\frac{1}{4}})^3\)

Substitute \(16^{\frac{1}{4}} = 2\) into \((16^{\frac{1}{4}})^3\), we get \(2^3 = 8\).

Answer:

8 (the option with the number 8)