How do you simplify $100^{- \frac{1}{2}}$ $100^(-1/2)$ ?

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How do you simplify $100^{- \frac{1}{2}}$ $100^(-1/2)$ ?

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Answer 1 · 2016-08-26T13:32:32

$\frac{1}{{(100)}^{0.5}}$ $1/(100)^0.5$

Explanation:

$\frac{1}{{(100)}^{0.5}} = \frac{1}{10}$ $1/(100)^0.5 = 1/10$

$= 0.1$ $=0.1$

Answer 2 · 2016-08-26T13:55:30

$\frac{1}{10}$ $1/10$

Explanation:

There are 2 different laws of indices being used here.

A negative index $\leftarrow use the reciprocal$ $larr "use the reciprocal"$
A fraction in the index $\leftarrow same as a root$ $larr " same as a root"$

It does not matter which law you apply first.
I prefer to get rid of the negative index first.

$100^{- \frac{1}{2}} = \frac{1}{100^{\frac{1}{2}}}$ $100^(-1/2) = 1/(100^(1/2))$

$\frac{1}{100^{\frac{1}{2}}} = \frac{1}{\sqrt{100}}$ $1/(100^(1/2)) = 1/sqrt100$

= $\frac{1}{10}$ $1/10$

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How do you simplify $100^{- \frac{1}{2}}$ $100^(-1/2)$ ?

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