Which expression is equal to 8?

Question

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