Question

Which expression is equivalent to StartFraction (3 m Superscript negative 1 Baseline n squared) Superscript negative 4 Baseline Over (2 m Superscript negative 2 Baseline n) cubed EndFraction?

Answer 1

Answer:

$3m^{10}n^{-11}$

Step-by-step explanation:

Given the expression $\frac{(3m^{-1}n^{2})^{-4} }{(2m^{-2}n)^{3} }$, we will use laws of indices to get the equivalent expression as shown below;

According to one of the law of indices,

$\frac{a^{m} }{a^{n} } = a^{m-n} \ and\ (a^{m})^{n} = a^{mn}$

$\frac{(3m^{-1}n^{2})^{-4} }{(2m^{-2}n)^{3} }\\= \frac{3m^{4}n^{-8} }{2m^{-6}n^{3} }\\= 3m^{(4-(-6))} * n^{-8-3}\\ = 3m^{10}n^{-11}$

This gives the required expression

Answer 2

Which expression is equivalent to StartFraction (3 m Superscript negative 1 Baseline n squared) Superscript negative 4 Baseline Over (2 m Superscript negative 2 Baseline n) cubed EndFraction? Assume mc024-2.jpg.
2 m squared n Superscript 5
StartFraction 81 m squared n Superscript 5 Baseline Over 8 EndFraction
2 m squared n squared
StartFraction 81 m squared n squared Over 8 EndFraction