Question

which expression is equivalent to \\(\frac{x^{\frac{4}{3}}}{x^{\frac{1}{3}}}\\)?

a. \\(x^{\frac{1}{4}}\\)

b. \\(x^{\frac{4}{9}}\\)

c. \\(x\\)

d. \\(x^{\frac{5}{3}}\\)

e. \\(x^4\\)

Explanation:

Step1: Recall exponent rule for division

When dividing exponents with the same base \(a^m\div a^n=a^{m - n}\), here base is \(x\), \(m=\frac{4}{3}\), \(n = \frac{1}{3}\).

Step2: Apply the rule

Calculate \(\frac{4}{3}-\frac{1}{3}=\frac{4 - 1}{3}=\frac{3}{3}=1\). So \(x^{\frac{4}{3}}\div x^{\frac{1}{3}}=x^{1}=x\).

Answer:

C. \(x\)