Question

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

Explanation:

Step1: Recall exponent rules

The expression is \( 16^{\frac{3}{4}} \). We use the rule \( a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m \).

Step2: Simplify the root first

First, find the 4th root of 16. Since \( 2^4 = 16 \), \( \sqrt[4]{16}=2 \).

Step3: Raise to the power of 3

Now raise this result to the power of 3: \( 2^3 = 8 \).

Answer:

8