Question

Simplify$\frac{30a^{-2}{b}^{-6}}{60a^{-6}{b}^{-8}}$ assuming that no variable equal to 0 .

Short answer

The simplified value of expression is $\frac{a^4{b}^2}{2}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression to simplify is$\frac{30a^{-2}{b}^{-6}}{60a^{-6}{b}^{-8}}$ .

Step 2. Simplify the given expression.

Simplifying$\frac{30a^{-2}{b}^{-6}}{60a^{-6}{b}^{-8}}$ gives,

$\begin{array}{c}\frac{30a^{-2}{b}^{-6}}{60a^{-6}{b}^{-8}}=\frac{a^{-2}{b}^{-6}}{2a^{-6}{b}^{-8}}\\ =\frac{{\left(a\right)}^{-2-(-6)}{\left(b\right)}^{-6-(-8)}}{2}\mathrm{....}(\text{Using}\frac{x^a}{x^b}=x^{a-b})\\ =\frac{{\left(a\right)}^4{\left(b\right)}^2}{2}\\ =\frac{a^4{b}^2}{2}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{a^4{b}^2}{2}$.