Question

Which expression is equal to 8?

Answer options with 5 options
A.
left-parenthesis 2 Superscript StartFraction 1 over 4 EndFraction Baseline right-parenthesis Superscript 4 Baseline

B.
left-parenthesis 4 Superscript StartFraction 1 over 2 EndFraction Baseline right-parenthesis Superscript 2 Baseline

C.
left-parenthesis 6 Superscript StartFraction 1 over 3 EndFraction Baseline right-parenthesis Superscript 3 Baseline

D.
left-parenthesis 8 Superscript StartFraction 1 over 2 EndFraction Baseline right-parenthesis Superscript 2 Baseline

E.
left-parenthesis 16 Superscript StartFraction 1 over 4 EndFraction Baseline right-parenthesis Superscript 4 Baseline

Answer 1

To determine which expression equals 8, let's evaluate each option:

**A. \((2^{\frac{1}{4}})^4\)**
Using the power of a power property \((a^m)^n = a^{m \cdot n}\):
\[
(2^{\frac{1}{4}})^4 = 2^{\frac{1}{4} \cdot 4} = 2^1 = 2
\]

**B. \((4^{\frac{1}{2}})^2\)**
\[
(4^{\frac{1}{2}})^2 = 4^{\frac{1}{2} \cdot 2} = 4^1 = 4
\]

**C. \((6^{\frac{1}{3}})^3\)**
\[
(6^{\frac{1}{3}})^3 = 6^{\frac{1}{3} \cdot 3} = 6^1 = 6
\]

**D. \((8^{\frac{1}{2}})^2\)**
\[
(8^{\frac{1}{2}})^2 = 8^{\frac{1}{2} \cdot 2} = 8^1 = 8
\]

**E. \((16^{\frac{1}{4}})^4\)**
\[
(16^{\frac{1}{4}})^4 = 16^{\frac{1}{4} \cdot 4} = 16^1 = 16
\]

From the evaluations above, the expression that equals 8 is:

**D. \((8^{\frac{1}{2}})^2\)**