Which expression is equivalent to StartFraction x Superscript StartFraction 4 over 3 EndFraction Baseline over x Superscript StartFraction 1 over 3 EndFraction Baseline EndFraction?

Question

Answer options with 5 options
A.
x Superscript StartFraction 1 over 4 EndFraction Baseline

B.
x Superscript StartFraction 4 over 9 EndFraction Baseline

C.
x

D.
x Superscript StartFraction 5 over 3 EndFraction Baseline

E.
x Superscript 4 Baseline

Answer 1

To simplify the expression \(\frac{x^{\frac{4}{3}}}{x^{\frac{1}{3}}}\), we can use the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\).

Applying this property, we have:

\[ \frac{x^{\frac{4}{3}}}{x^{\frac{1}{3}}} = x^{\frac{4}{3} - \frac{1}{3}} = x^{\frac{4 - 1}{3}} = x^{\frac{3}{3}} = x^1 = x \]

Thus, the expression simplifies to \(x\).

The correct answer is: C. \(x\).