How do you simplify ${(- w^{2})}^{- 5}$ $(-w^ 2)^ -5$ ?

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Answer 1 · 2015-09-30T10:42:21

${(- w^{2})}^{- 5} = - w^{- 10}$ $(−w^2)^-5 = color(green)(-w^(-10)$

${(- w^{2})}^{- 5}$ $(−w^2)^-5$

By property
$a^{- m} = \frac{1}{a^{m}}$ $color(blue)(a^(-m)=1/a^m$

Applying the same:

$= \frac{1}{{(- w^{2})}^{5}}$ $=1/(-w^2)^5$

$= \frac{1}{{(- 1 \cdot w^{2})}^{5}}$ $=1/(-1*w^2)^5$

By property
${(a \cdot b)}^{m} = a^{m} \cdot b^{m}$ $color(blue)((a*b)^m = a^m *b^m$

Applying the same:

$= \frac{1}{{(- 1)}^{5} \cdot {(w^{2})}^{5}}$ $=1/((−1)^5*(w^2)^5)$

By property
${(a^{m})}^{n} = a^{m \cdot n}$ $color(blue)((a^m)^n = a^(m*n)$

Applying the same:
$= \frac{1}{(- 1) \cdot w^{2 \cdot 5}}$ $=1/((-1)*w^(2*5)$

$= - \frac{1}{w^{10}}$ $= -1/w^10$

$= - w^{- 10}$ $= color(green)(-w^(-10)$

How do you simplify (−w2)−5(-w^ 2)^ -5?