Question

which of the following is equivalent to ( 16^{\frac{3}{4}} )?

○ 6

○ 8

○ 12

○ 64

Explanation:

Step1: Recall exponent rule

The exponent rule for \(a^{\frac{m}{n}}\) is \(a^{\frac{m}{n}}=\sqrt[n]{a^m}\) or \((\sqrt[n]{a})^m\). For \(16^{\frac{3}{4}}\), we can rewrite it as \((\sqrt[4]{16})^3\).

Step2: Calculate the fourth root of 16

\(\sqrt[4]{16}\) means finding a number \(x\) such that \(x^4 = 16\). We know that \(2^4=16\), so \(\sqrt[4]{16}=2\).

Step3: Raise the result to the power of 3

Now we have \((2)^3\). Calculating \(2^3\), we get \(2\times2\times2 = 8\).

Answer:

8 (assuming the base is 16, as 10^(3/4) is not 8, 6, 12 or 64. Likely a typo, base should be 16. So the equivalent value is 8)