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Brilliant_brown [7]
3 years ago
15

Simplify 25^ - 1/2 Please explain! I know the answer is 1/5 but why?

Mathematics
1 answer:
lisov135 [29]3 years ago
3 0

(25)^{-\frac{1}{2} }

When the exponent is negative, you have to make the number a fraction(1 over the number).

For example:

25^{-2} = \frac{1}{25^{2} }

x^{-1} =\frac{1}{x^{1}  }

This gets rid of the negative, but it leaves the exponent

(25)^{-\frac{1}{2}}  = \frac{1}{25^{1/2}}

When an exponent is a fraction, it is the square root.

For example:

x^{\frac{1}{3}} =  \sqrt[3]{x}

x^{\frac{1}{2}}  =\sqrt{x}

x^{\frac{1}{4}}=\sqrt[4]{x}

So...

\frac{1}{25^{1/2}} = \frac{1}{\sqrt{25}  } = \frac{1}{5}

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