How do you multiply $(4 m^{- 6} n^{10}) (- 10 m^{- 2} n^{3})$ $(4m ^ { - 6} n ^ { 10} ) ( - 10m ^ { - 2} n ^ { 3} )$ ?

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How do you multiply $(4 m^{- 6} n^{10}) (- 10 m^{- 2} n^{3})$ $(4m ^ { - 6} n ^ { 10} ) ( - 10m ^ { - 2} n ^ { 3} )$ ?

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Answer 1 · 2016-11-05T06:39:58

By multiplying like terms.

Explanation:

So here you have $(4 m^{- 6} n^{10}) (- 10 m^{- 2} n^{3})$ $(4m^-6n^10)(-10m^-2n^3)$ .

Essentially you just add the exponents on the like terms (add the exponents on the m's and n's) and then multiply the constants.

$4 \cdot - 10 = - 40$ $4*-10=-40$
$m^{- 6} \cdot m^{- 2} = m^{- 6 + (- 2)} = m^{- 8}$ $m^-6*m^-2=m^(-6+(-2))=m^-8$
$n^{10} \cdot n^{3} = n^{10 + 3} = n^{13}$ $n^10*n^3=n^(10+3)=n^13$

Put this all together and you get

$- 40 m^{- 8} n^{13}$ $-40m^-8n^13$

To make it look prettier you could say

$\frac{- 40 n^{13}}{m^{8}}$ $(-40n^13)/m^8$

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How do you multiply $(4 m^{- 6} n^{10}) (- 10 m^{- 2} n^{3})$ $(4m ^ { - 6} n ^ { 10} ) ( - 10m ^ { - 2} n ^ { 3} )$ ?

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Explanation:

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How do you multiply $(4 m^{- 6} n^{10}) (- 10 m^{- 2} n^{3})$ $(4m ^ { - 6} n ^ { 10} ) ( - 10m ^ { - 2} n ^ { 3} )$ ?