Q. 40 - Algebra 2

Question

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

Step-by-Step Solution

Answer

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

Step 1. Write down the given expression.

The given expression to simplify is $\frac{30a^{-2}{b}^{-6}}{60a^{-6}{b}^{-8}}$$\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 $\frac{a^4{b}^2}{2}$ .