Question

simplify. assume all variables are positive.
\\(\frac{b^{\frac{2}{3}}}{b^{\frac{4}{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: Use exponent - division rule

When dividing two powers with the same base $b^m\div b^n=b^{m - n}$. Here, $m=\frac{2}{3}$ and $n = \frac{4}{3}$, so $\frac{b^{\frac{2}{3}}}{b^{\frac{4}{3}}}=b^{\frac{2}{3}-\frac{4}{3}}$.

Step2: Calculate the exponent

$\frac{2}{3}-\frac{4}{3}=\frac{2 - 4}{3}=\frac{- 2}{3}$. So, $b^{\frac{2}{3}-\frac{4}{3}}=b^{-\frac{2}{3}}$.

Step3: Make the exponent positive

Using the rule $b^{-n}=\frac{1}{b^{n}}$, we rewrite $b^{-\frac{2}{3}}$ as $\frac{1}{b^{\frac{2}{3}}}$.

Answer:

$\frac{1}{b^{\frac{2}{3}}}$