Question

simplify. assume all variables are positive.\\(\frac{w^{\frac{7}{3}}}{w^{\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 like bases, subtract exponents: $\frac{w^m}{w^n}=w^{m-n}$
$\frac{w^{\frac{7}{3}}}{w^{\frac{1}{3}}}=w^{\frac{7}{3}-\frac{1}{3}}$

Step2: Subtract the fractions

Calculate the exponent difference.
$w^{\frac{7-1}{3}}=w^{\frac{6}{3}}$

Step3: Simplify the exponent

Reduce the fraction in the exponent.
$w^{2}$

Answer:

$w^2$