Question

simplify. assume all variables are positive.
\\(\frac{x^{\frac{8}{3}}}{x^{\frac{1}{3}}}\\)
write your answer in the form a or \\(\frac{a}{b}\\) where a and b are constants or variable expressions that have no variables in common. all exponents in your answer should be positive.

Explanation:

Step1: Apply exponent - division rule

When dividing two terms with the same base \(a^m\div a^n=a^{m - n}\), here \(a = x\), \(m=\frac{8}{3}\), and \(n=\frac{1}{3}\). So \(x^{\frac{8}{3}}\div x^{\frac{1}{3}}=x^{\frac{8}{3}-\frac{1}{3}}\).

Step2: Calculate the exponent

\(\frac{8}{3}-\frac{1}{3}=\frac{8 - 1}{3}=\frac{7}{3}\). So \(x^{\frac{8}{3}-\frac{1}{3}}=x^{\frac{7}{3}}\).

Answer:

\(x^{\frac{7}{3}}\)