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:

`$(9 m^(-3) p^(-6))/(4 s^(-2))`

To write this expression without negative exponents:

`$(9 m^(-3) p^(-6))/(4 s^(-2))`

Using exponent rule:
`a^(-b)=(1)/(a^b)`

`$m^(-3)=(1)/(m^3)`

`$p^(-6)=(1)/(p^6)`

`$s^(-2)=(1)/(s^2)`

Substitute these in the expression.

`$(9 m^(-3) p^(-6))/(4 s^(-2))=(9 (1)/(m^3) (1)/(p^6) )/(4 (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 * {s^2} }{4 {m^3}*{p^6}}`

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

Option B is the correct answer.

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