Option B:
[tex]$\frac{9{s^2} }{4 {m^3} {p^6}}[/tex]
Solution:
Given expression:
[tex]$\frac{9 m^{-3} p^{-6}}{4 s^{-2}}[/tex]
To write this expression without negative exponents:
[tex]$\frac{9 m^{-3} p^{-6}}{4 s^{-2}}[/tex]
Using exponent rule: [tex]a^{-b}=\frac{1}{a^b}[/tex]
[tex]$m^{-3}=\frac{1}{m^3}[/tex]
[tex]$p^{-6}=\frac{1}{p^6}[/tex]
[tex]$s^{-2}=\frac{1}{s^2}[/tex]
Substitute these in the expression.
[tex]$\frac{9 m^{-3} p^{-6}}{4 s^{-2}}=\frac{9 \frac{1}{m^3} \frac{1}{p^6} }{4 \frac{1}{s^2} }[/tex]
Denominator of fraction in denominator goes to numerator.
Denominator of fraction in numerator goes to denominator.
Therefore, [tex]s^2[/tex] goes to numerator and [tex]m^3p^6[/tex] goes to denominator.
[tex]$=\frac{9 \times {s^2} }{4 {m^3}\times{p^6}}[/tex]
[tex]$=\frac{9{s^2} }{4 {m^3} {p^6}}[/tex]
Option B is the correct answer.
[tex]$\frac{9 m^{-3} p^{-6}}{4 s^{-2}}=\frac{9{s^2} }{4 {m^3} {p^6}}[/tex]
