What is (-2m^2*n^{-3}*p^4)^5 ?

The solution to (-2m^2*n^{-3}*p^4)^5 is -(32m^{10}p^{20})/(n^{15)}

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simplify (-2m^2n^{-3}p^4)^5

simplify

(- 2 m^{2} \cdot n^{- 3} \cdot p^{4})^{5}

- \frac{32 m ^{10} p ^{20}}{n ^{15}}

Solution steps

(- 2 m^{2} n^{- 3} p^{4})^{5}

Apply exponent rule:

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

n

is odd

(- 2 m^{2} n^{- 3} p^{4})^{5} = - (2 m^{2} n^{- 3} p^{4})^{5}

= - (2 m^{2} n^{- 3} p^{4})^{5}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2 m^{2} n^{- 3} p^{4})^{5} = 2^{5} (m^{2})^{5} (n^{- 3})^{5} (p^{4})^{5}

= - 2^{5} (m^{2})^{5} (n^{- 3})^{5} (p^{4})^{5}

2^{5} = 32

= - 32 (m^{2})^{5} (n^{- 3})^{5} (p^{4})^{5}

Simplify

(m^{2})^{5} : m^{10}

= - 32 m^{10} (n^{- 3})^{5} (p^{4})^{5}

Simplify

(n^{- 3})^{5} : \frac{1}{n ^{15}}

= - 32 m^{10} \frac{1}{n ^{15}} (p^{4})^{5}

Simplify

(p^{4})^{5} : p^{20}

= - 32 m^{10} \frac{1}{n ^{15}} p^{20}

Simplify

32 m^{10} \frac{1}{n ^{15}} p^{20} : \frac{32 m ^{10} p ^{20}}{n ^{15}}

= - \frac{32 m ^{10} p ^{20}}{n ^{15}}

- \frac{1}{4} \cdot \frac{180}{x}

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\frac{1 2 ^{3 m}}{( 2 ^{3 m} ) \cdot 9 ^{- 2 m}}

8 (x + y)^{3} - 50 (x + y)

\frac{1}{( 1 - \frac{e}{x ^{2}} )}

What is (-2m^2*n^{-3}*p^4)^5 ?
The solution to (-2m^2*n^{-3}*p^4)^5 is -(32m^{10}p^{20})/(n^{15)}