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

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

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Answer 1 · 2016-03-10T11:59:23

$- \frac{1}{25} or - 0.04$ $color(blue)(-1/25 or -0.04)$

Explanation:

$- 5^{- 2}$ $-5^-2$

since, $x^{- 1} = \frac{1}{x}$ $x^-1 = 1/x$ ,

therefore,

$\frac{1}{{- 5}^{2}}$ $1/-5^2$

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

= $- \frac{1}{25}$ $-1/25$

Is the final answer :D

If the negative was meant to be part of the power, one would need to write ${(- 5)}^{- 2}$ $(-5)^-2$

Answer 2 · 2016-03-10T12:27:21

$- 0.04$ $-0.04$

Explanation:

$- 5^{- 2}$ $-5^-2$

Remember $a^{- n} = \frac{1}{a^{n}}$ $a^-n=1/(a^n)$

and that $- a = (- 1) \cdot a$ $-a=(-1)*a$

since the order of operations has us do powers before multiplication, the power does not affect the $- 1$ $-1$ . The other way to look at it is that the power $5^{- 2}$ $5^-2$ is being subtracted, in which case the order of operations also tells us to do the power before the subtraction:

$:.-5^-2=(-1)*1/(5)^2$

$=-1/((5)(5))$

$=-1/25=0.04$

If the negative was meant to be included in the power, it would need to be written as $(-5)^-2$

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

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