Question

Simplify$\frac{12x^{-3}{y}^{-2}{z}^{-8}}{30x^{-6}{y}^{-4}{z}^{-1}}$ assuming that no variable equal to 0 .

Short answer

The simplified value of expression is $\frac{2x^3{y}^2{z}^{-7}}{5}$.

Step-by-step solution

Step 1. Write down the given expression.

The given expression to simplify is $\frac{12x^{-3}{y}^{-2}{z}^{-8}}{30x^{-6}{y}^{-4}{z}^{-1}}$.

Step 2. Simplify the given expression.

Simplifying $\frac{12x^{-3}{y}^{-2}{z}^{-8}}{30x^{-6}{y}^{-4}{z}^{-1}}$gives,

$\begin{array}{c}\frac{12x^{-3}{y}^{-2}{z}^{-8}}{30x^{-6}{y}^{-4}{z}^{-1}}=\frac{2x^{-3}{y}^{-2}{z}^{-8}}{5x^{-6}{y}^{-4}{z}^{-1}}\\ =\frac{2x^{-3-(-6)}{y}^{-2-(-4)}{z}^{-8-(-1)}}{5}\mathrm{....}(\text{Using}\frac{x^a}{x^b}=x^{a-b})\\ =\frac{2x^3{y}^2{z}^{-7}}{5}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{2x^3{y}^2{z}^{-7}}{5}$.