Question

Which of the following expression represents the area of a rectangle with $5p^3{q}^2$ as length and $5^7{p}^2{q}^4$ as width?

• A. $8^5{p}^5{q}^6$
• B. $5^8{p}^5{q}^6$
• C. $5^7{p}^5{q}^6$
• D. $5^8{p}^6{q}^5$

Answer 1

The correct option is B $5^8{p}^5{q}^6$

Given:
$\bullet$ Length of rectangle $=5p^3{q}^2$
$\bullet$ Width of rectangle $=5^7{p}^2{q}^4$

And, as given in the hint,
Area of rectangle $=$ Length $\times$ Width

$=5^1{p}^3{q}^2\times 5^7{p}^2{q}^4$

$=5^{(1+7)}{p}^{(3+2)}{q}^{(2+4)}$
[$\because a^m\times a^n=a^{(m+n)}$ ]

$=5^8{p}^5{q}^6$

$\therefore$ The area of rectangle with length $5p^3{q}^2$ and width $5^7{p}^2{q}^4$ is $5^8{p}^5{q}^6.$

Therefore, option (b.) is the correct one.