What is ((m^{-2}n)/(2mn^3))^2 ?

The solution to ((m^{-2}n)/(2mn^3))^2 is 1/(4m^6n^4)

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simplify ((m^{-2}n)/(2mn^3))^2

simplify

(\frac{m ^{- 2} n}{2 m n ^{3}})^{2}

\frac{1}{4 m ^{6} n ^{4}}

Solution steps

(\frac{m ^{- 2} n}{2 m n ^{3}})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( m ^{- 2} n ) ^{2}}{( 2 m n ^{3} ) ^{2}}

Simplify

(m^{- 2} n)^{2} : \frac{n ^{2}}{m ^{4}}

= \frac{\frac{n ^{2}}{m ^{4}}}{( 2 m n ^{3} ) ^{2}}

Simplify

(2 m n^{3})^{2} : 4 m^{2} n^{6}

= \frac{\frac{n ^{2}}{m ^{4}}}{4 m ^{2} n ^{6}}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{n ^{2}}{m ^{4} \cdot 4 m ^{2} n ^{6}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{n ^{2}}{n ^{6}} = \frac{1}{n ^{6 - 2}}

= \frac{1}{4 m ^{4} m ^{2} n ^{6 - 2}}

Subtract the numbers:

6 - 2 = 4

= \frac{1}{4 m ^{4} m ^{2} n ^{4}}

4 m^{4} m^{2} n^{4} = 4 m^{6} n^{4}

= \frac{1}{4 m ^{6} n ^{4}}

2 - [- 2 (x + 1) - \frac{x - 3}{2}] = \frac{2 x}{3} - \frac{5 x - 3}{12} + 3 x

12 = - 3 (x + 2)

(9 + 3 i) (9 - 3 i)

3 x + 2 + 5 (x - 1) = 8 x + 17

\frac{3}{5} x + \frac{2}{5} - \frac{3}{10} = \frac{1}{3} - \frac{1}{15} + \frac{1}{6} x

What is ((m^{-2}n)/(2mn^3))^2 ?
The solution to ((m^{-2}n)/(2mn^3))^2 is 1/(4m^6n^4)