What is (2mn^2(3m^2n)^2)/(12m^3n^4) ?

The solution to (2mn^2(3m^2n)^2)/(12m^3n^4) is (3m^2)/2

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simplify (2mn^2(3m^2n)^2)/(12m^3n^4)

simplify

\frac{2 m n ^{2} ( 3 m ^{2} n ) ^{2}}{12 m ^{3} n ^{4}}

\frac{3 m ^{2}}{2}

Solution steps

\frac{2 m n ^{2} ( 3 m ^{2} n ) ^{2}}{12 m ^{3} n ^{4}}

Factor the number:

12 = 2 \cdot 6

= \frac{2 m n ^{2} ( 3 m ^{2} n ) ^{2}}{2 \cdot 6 m ^{3} n ^{4}}

Cancel the common factor:

2

= \frac{m n ^{2} ( 3 m ^{2} n ) ^{2}}{6 m ^{3} n ^{4}}

Simplify

\frac{m}{m ^{3}} : \frac{1}{m ^{2}}

= \frac{n ^{2} ( 3 m ^{2} n ) ^{2}}{6 m ^{2} n ^{4}}

Simplify

\frac{n ^{2}}{n ^{4}} : \frac{1}{n ^{2}}

= \frac{( 3 m ^{2} n ) ^{2}}{6 m ^{2} n ^{2}}

Simplify

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

= \frac{3 ^{2} m ^{4} n ^{2}}{6 m ^{2} n ^{2}}

Factor the number:

6 = 3 \cdot 2

= \frac{3 ^{2} m ^{4} n ^{2}}{3 \cdot 2 m ^{2} n ^{2}}

\frac{3 ^{2}}{3} = 3

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

Cancel the common factor:

n^{2}

= \frac{3 m ^{4}}{2 m ^{2}}

Simplify

\frac{m ^{4}}{m ^{2}} : m^{2}

= \frac{3 m ^{2}}{2}

lo g_{3} (\frac{1}{27}) = x

- \frac{2}{3} - \frac{7}{9}

∣ 3.1416 - 7 ∣ > 3

(2 i - 3) - (7 + \frac{1}{5} i)

(5 x + 20) (x - 5) = 0

What is (2mn^2(3m^2n)^2)/(12m^3n^4) ?
The solution to (2mn^2(3m^2n)^2)/(12m^3n^4) is (3m^2)/2