How do you use laws of exponents to simplify ${(- m n^{8})}^{2}$ $(-mn^8)^2$ ?

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Answer 1 · 2015-08-05T06:23:44

$= - m^{2} n^{16}$ $=color(green)(−m^2n^16$

${(- m n^{8})}^{2}$ $(−mn^8)^color(blue)(2$

As per property:
${(a b)}^{m} = a^{m} \cdot b^{m}$ $color(blue)((ab)^m =a^m * b^m$

Applying the same property to the expression, the exponent $2$ $color(blue)(2$ is multiplied with each term within the bracket.

$= (- m^{2}) (n^{8 \cdot 2})$ $=(−m^color(blue)(2))(n^(8 * color(blue)(2)))$

$= - m^{2} n^{16}$ $=color(green)(−m^2n^16$

How do you use laws of exponents to simplify (-mn^8)^2(−mn8)2(-mn^8)^2?