What is 100*100^{-2/pi} ?

The solution to 100*100^{-2/pi} is 100^{(pi-2)/pi}

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simplify 100*100^{-2/pi}

simplify

100 \cdot 10 0^{- \frac{2}{π}}

10 0^{\frac{π - 2}{π}}

Decimal Notation

5.33040 \dots

Solution steps

100 \cdot 10 0^{- \frac{2}{π}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= 100 \cdot \frac{1}{10 0 ^{\frac{2}{π}}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 100}{10 0 ^{\frac{2}{π}}}

Multiply the numbers:

1 \cdot 100 = 100

= \frac{100}{10 0 ^{\frac{2}{π}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{100}{10 0 ^{\frac{2}{π}}} = 10 0^{1 - \frac{2}{π}}

= 10 0^{1 - \frac{2}{π}}

Subtract the numbers:

1 - \frac{2}{π} = \frac{π - 2}{π}

= 10 0^{\frac{π - 2}{π}}

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