What is ((-2m^2n^5)^4)/((12m^3n^5)^3) ?

The solution to ((-2m^2n^5)^4)/((12m^3n^5)^3) is (n^5)/(108m)

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simplify ((-2m^2n^5)^4)/((12m^3n^5)^3)

simplify

\frac{( - 2 m ^{2} n ^{5} ) ^{4}}{( 12 m ^{3} n ^{5} ) ^{3}}

\frac{n ^{5}}{108 m}

Solution steps

\frac{( - 2 m ^{2} n ^{5} ) ^{4}}{( 12 m ^{3} n ^{5} ) ^{3}}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 2 m^{2} n^{5})^{4} = (2 m^{2} n^{5})^{4}

= \frac{( 2 m ^{2} n ^{5} ) ^{4}}{( 12 m ^{3} n ^{5} ) ^{3}}

Simplify

(2 m^{2} n^{5})^{4} : 2^{4} m^{8} n^{20}

= \frac{2 ^{4} m ^{8} n ^{20}}{( 12 m ^{3} n ^{5} ) ^{3}}

Simplify

(12 m^{3} n^{5})^{3} : 1 2^{3} m^{9} n^{15}

= \frac{2 ^{4} m ^{8} n ^{20}}{1 2 ^{3} m ^{9} n ^{15}}

Factor

1 2^{3} : 2^{6} \cdot 3^{3}

= \frac{2 ^{4} m ^{8} n ^{20}}{2 ^{6} \cdot 3 ^{3} m ^{9} n ^{15}}

\frac{2 ^{4}}{2 ^{6}} = \frac{1}{2 ^{2}}

= \frac{m ^{8} n ^{20}}{2 ^{2} \cdot 3 ^{3} m ^{9} n ^{15}}

Simplify

\frac{n ^{20}}{n ^{15}} : n^{5}

= \frac{m ^{8} n ^{5}}{2 ^{2} \cdot 3 ^{3} m ^{9}}

Simplify

\frac{m ^{8}}{m ^{9}} : \frac{1}{m}

= \frac{n ^{5}}{2 ^{2} \cdot 3 ^{3} m}

Simplify

2^{2} \cdot 3^{3} m : 108 m

= \frac{n ^{5}}{108 m}

20 \times 5

(2 x + 5) \cdot (2 x - 5)

12 x^{2} - 24 x

e^{x l n (2)}

lo g_{10} (4) (2)

What is ((-2m^2n^5)^4)/((12m^3n^5)^3) ?
The solution to ((-2m^2n^5)^4)/((12m^3n^5)^3) is (n^5)/(108m)