Q32. - Algebra 2

Question

Simplify  $\frac{-5x^3{y}^3{z}^4}{20x^3{y}^7{z}^4}$ assuming that no variable equal to  0.

Step-by-Step Solution

Answer

The simplified value of expression is $-\frac{y^{-4}}{4}$ .

Step 1. Write down the given expression.

The given expressiomn to simplify is $\frac{-5x^3{y}^3{z}^4}{20x^3{y}^7{z}^4}$ .

Step 2. Simplify the given expression.

Simplifying $\frac{-5x^3{y}^3{z}^4}{20x^3{y}^7{z}^4}$  gives,

$\begin{array}{c}\frac{-5x^3{y}^3{z}^4}{20x^3{y}^7{z}^4}=\frac{(-5){\left(x\right)}^3{\left(y\right)}^3{\left(z\right)}^4}{\left(20\right){\left(x\right)}^3{\left(y\right)}^7{\left(z\right)}^4}\\ =\frac{(-1){\left(x\right)}^{3-3}{\left(y\right)}^{3-7}{\left(z\right)}^{4-4}}{4}\mathrm{....}(\text{Using }\frac{x^a}{x^b}=x^{a-b})\\ =-\frac{{\left(x\right)}^0{\left(y\right)}^{-4}{\left(z\right)}^0}{4}\\ =-\frac{y^{-4}}{4}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $-\frac{y^{-4}}{4}$ .