Q33. - Algebra 2

Question

Simplify  $\frac{3a^5{b}^3{c}^3}{9a^3{b}^{7}c}$ assuming that no variable equal to  0.

Step-by-Step Solution

Answer

The simplified value of expression is  $\frac{a^2{b}^{-4}{c}^2}{3}$.

Step 1. Write down the given expression.

The given expression to simplify is $\frac{3a^5{b}^3{c}^3}{9a^3{b}^{7}c}$ .

Step 2. Simplify the given expression.

Simplifying  $\frac{3a^5{b}^3{c}^3}{9a^3{b}^{7}c}$ gives,

$\begin{array}{c}\frac{3a^5{b}^3{c}^3}{9a^3{b}^{7}c}=\frac{\left(3\right)\left(a^5{b}^3{c}^3\right)}{\left(9\right)\left(a^3{b}^{7}c\right)}\\ =\frac{\left(a^{5-3}{b}^{3-7}{c}^{3-1}\right)}{3}\mathrm{....}(\text{Using }\frac{x^a}{x^b}=x^{a-b})\\ =\frac{\left(a^2{b}^{-4}{c}^2\right)}{3}\\ =\frac{a^2{b}^{-4}{c}^2}{3}\end{array}$

Step 3. Conclusion.

The simplified value of expression is $\frac{a^2{b}^{-4}{c}^2}{3}$ .