Chapter 7.2, Problem 70PFA

To determine

To Find: The exponent of variable ‘d’ in simplified expression of ${\left(\frac{8b^5{c}^4{d}^9}{2b^7{c}^2{d}^5}\right)}^3$

Answer to Problem 70PFA

The exponent of variable $d\text{ is }12$ option ‘B’ is correct.

Explanation of Solution

Given information:

The expression ${\left(\frac{8b^5{c}^4{d}^9}{2b^7{c}^2{d}^5}\right)}^3$

Concept and Formula Used:

Rule of exponent.

  $a^{-n}=\frac{1}{a^n},a^0=1,\frac{a^m}{a^n}=a^{m-n}$

Calculation:

The given expression is

  $\begin{array}{l}{\left(\frac{8b^5{c}^4{d}^9}{2b^7{c}^2{d}^5}\right)}^3\\ \text{Using }\frac{a^m}{a^n}=a^{m-n}\\ {\left(\frac{8b^5{c}^4{d}^9}{2b^7{c}^2{d}^5}\right)}^3={\left(4b^{5-7}{c}^{4-2}{d}^{9-5}\right)}^3\\ {\left(\frac{8b^5{c}^4{d}^9}{2b^7{c}^2{d}^5}\right)}^3={\left(4b^{-2}{c}^2{d}^4\right)}^3\\ \text{Using }{\left(a^m\right)}^n=a^{m\times n}\\ {\left(\frac{8b^5{c}^4{d}^9}{2b^7{c}^2{d}^5}\right)}^3=\left(4^3{b}^{-2\times 3}{c}^{2\times 3}{d}^{4\times 3}\right)\\ {\left(\frac{8b^5{c}^4{d}^9}{2b^7{c}^2{d}^5}\right)}^3=\left(64b^{-6}{c}^6{d}^{12}\right)\end{array}$

Conclusion:

The exponent of variable $d\text{ is }12$ option ‘B’ is correct.