Question

simplify. assume all variables are positive.
$c^{\frac{5}{6}} \div c^{\frac{7}{6}}$
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: Recall exponent rule for division

When dividing two exponential expressions with the same base, we subtract the exponents: $a^m \div a^n = a^{m - n}$. So for $c^{\frac{5}{6}} \div c^{\frac{7}{6}}$, we have $c^{\frac{5}{6}-\frac{7}{6}}$.

Step2: Subtract the exponents

Calculate $\frac{5}{6}-\frac{7}{6}=\frac{5 - 7}{6}=\frac{-2}{6}=-\frac{1}{3}$. So now we have $c^{-\frac{1}{3}}$.

Step3: Rewrite negative exponent as positive

Using the rule $a^{-n}=\frac{1}{a^n}$, we can rewrite $c^{-\frac{1}{3}}$ as $\frac{1}{c^{\frac{1}{3}}}$.

Answer:

$\frac{1}{c^{\frac{1}{3}}}$