Question

Write the following expression without using negative exponents.

Answer 1

Option B:

$\frac{9{s^2} }{4 {m^3} {p^6}}$

Solution:

Given expression:

$\frac{9 m^{-3} p^{-6}}{4 s^{-2}}$

To write this expression without negative exponents:

$\frac{9 m^{-3} p^{-6}}{4 s^{-2}}$

Using exponent rule: $a^{-b}=\frac{1}{a^b}$

$m^{-3}=\frac{1}{m^3}$

$p^{-6}=\frac{1}{p^6}$

$s^{-2}=\frac{1}{s^2}$

Substitute these in the expression.

$\frac{9 m^{-3} p^{-6}}{4 s^{-2}}=\frac{9 \frac{1}{m^3} \frac{1}{p^6} }{4 \frac{1}{s^2} }$

Denominator of fraction in denominator goes to numerator.

Denominator of fraction in numerator goes to denominator.

Therefore, $s^2$ goes to numerator and $m^3p^6$ goes to denominator.

               $=\frac{9 \times {s^2} }{4 {m^3}\times{p^6}}$

              $=\frac{9{s^2} }{4 {m^3} {p^6}}$

Option B is the correct answer.

$\frac{9 m^{-3} p^{-6}}{4 s^{-2}}=\frac{9{s^2} }{4 {m^3} {p^6}}$