Question #85def

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Question #85def

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Answer 1 · 2017-08-31T22:37:43

$\frac{{(- 5)}^{3}}{- 5^{3}} = 1$ $(-5)^3/(-5^3)=1$

Explanation:

$\frac{{(- 5)}^{3}}{- 5^{3}}$ $(-5)^3/(-5^3)$

The issue here is dealing with the negatives. We should note that the minus sign in the numerator is contained within the power of $3$ $3$ , whereas there is a single, standalone minus $1$ $1$ in the denominator which is multiplied by $5^{3}$ $5^3$ . Rewriting to clarify, then, we have:

$= \frac{{[- 1 (5)]}^{3}}{- 1 (5^{3})}$ $=([-1(5)]^3)/(-1(5^3))$

Distributing the power:

$= \frac{{(- 1)}^{3} 5^{3}}{- 1 (5^{3})}$ $=((-1)^3 5^3)/(-1(5^3))$

Note that ${(- 1)}^{3} = (- 1) (- 1) (- 1) = - 1$ $(-1)^3=(-1)(-1)(-1)=-1$ :

$= \frac{- 1 \cdot 5^{3}}{- 1 \cdot 5^{3}}$ $=(-1*5^3)/(-1*5^3)$

$= 1$ $=1$

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Question #85def

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