Question

5.2 properties of exponents homework
score: 8/25 answered: 9/26
question 10
rewrite without parentheses or negative exponents:
$left(\frac{b}{c}
ight)^{-3}=$

Explanation:

Step1: Apply negative - exponent rule

According to the rule $a^{-n}=\frac{1}{a^{n}}$, for $(\frac{b}{c})^{-3}$, we have $(\frac{b}{c})^{-3}=\frac{1}{(\frac{b}{c})^{3}}$.

Step2: Simplify the complex - fraction

Using the rule $(\frac{a}{b})^n=\frac{a^n}{b^n}$, $\frac{1}{(\frac{b}{c})^{3}}=\frac{1}{\frac{b^{3}}{c^{3}}}$. And $\frac{1}{\frac{b^{3}}{c^{3}}}=\frac{c^{3}}{b^{3}}$ (by the rule $\frac{1}{\frac{a}{b}}=\frac{b}{a}$).

Answer:

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