What is (-4m^2n)^4*1/6 m^{-10}n^{-4} ?

The solution to (-4m^2n)^4*1/6 m^{-10}n^{-4} is (128)/(3m^2)

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simplify (-4m^2n)^4*1/6 m^{-10}n^{-4}

simplify

(- 4 m^{2} n)^{4} \cdot \frac{1}{6} m^{- 10} n^{- 4}

\frac{128}{3 m ^{2}}

Solution steps

(- 4 m^{2} n)^{4} \frac{1}{6} m^{- 10} n^{- 4}

Simplify

(- 4 m^{2} n)^{4} : 256 m^{8} n^{4}

= 256 m^{8} n^{4} \frac{1}{6} m^{- 10} n^{- 4}

Apply exponent rule:

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

m^{- 10} = \frac{1}{m ^{10}}

= 256 m^{8} n^{4} \frac{1}{6} \cdot \frac{1}{m ^{10}} n^{- 4}

Apply exponent rule:

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

n^{- 4} = \frac{1}{n ^{4}}

= 256 m^{8} n^{4} \frac{1}{6} \cdot \frac{1}{m ^{10}} \cdot \frac{1}{n ^{4}}

Cross-cancel common factor:

n^{4}

= 256 m^{8} \frac{1}{6} \cdot \frac{1}{m ^{10}}

Apply the fraction rule:

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

= \frac{256 m ^{8} \cdot 1 \cdot 1}{6 m ^{10}}

Multiply the numbers:

256 \cdot 1 \cdot 1 = 256

= \frac{256 m ^{8}}{6 m ^{10}}

Factor the number:

256 = 2 \cdot 128

= \frac{2 \cdot 128 m ^{8}}{6 m ^{10}}

Factor the number:

6 = 2 \cdot 3

= \frac{2 \cdot 128 m ^{8}}{2 \cdot 3 m ^{10}}

Cancel the common factor:

2

= \frac{128 m ^{8}}{3 m ^{10}}

Simplify

\frac{m ^{8}}{m ^{10}} : \frac{1}{m ^{2}}

= \frac{128}{3 m ^{2}}

150 (\frac{π}{180})

∣ 4 w - 1 ∣ = 5 w + 37

x + 8 = 2 x + 1

- 15 - 2

24

What is (-4m^2n)^4*1/6 m^{-10}n^{-4} ?
The solution to (-4m^2n)^4*1/6 m^{-10}n^{-4} is (128)/(3m^2)