Q9. - Algebra 2

Question

Simplify $\frac{81p^6{q}^5}{{\left(3p^{2}q\right)}^2}$  assuming that no variable equal to  0.

Step-by-Step Solution

Answer

The simplified value of expression is $9p^2{q}^3$ .

Step 1. Write down the given expression.

The given expression to simplify is $\frac{81p^6{q}^5}{{\left(3p^{2}q\right)}^2}$ .

Step 2. Simplify the given expression.

Simplifying $\frac{81p^6{q}^5}{{\left(3p^{2}q\right)}^2}$  gives,

$\begin{array}{c}\frac{81p^6{q}^5}{{\left(3p^{2}q\right)}^2}=\frac{81p^6{q}^5}{{\left(3\right)}^2{\left(p^{2}q\right)}^2}\\ =\frac{9p^6{q}^5}{p^4{q}^2}\\ =9{\left(p\right)}^{6-4}{\left(q\right)}^{5-2}\mathrm{....}(\text{Using }\frac{x^a}{x^b}=x^{a-b})\\ =9p^2{q}^3\end{array}$

Step 3. Conclusion.

The simplified value of expression is $9p^2{q}^3$ .