What is 0.3*pi*((0.2)^{-2}-1)^{-1/12} ?

The solution to 0.3*pi*((0.2)^{-2}-1)^{-1/12} is 0.72319…

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simplify 0.3pi((0.2)^{-2}-1)^{-1/12}

simplify

0.3 \cdot π \cdot ((0.2)^{- 2} - 1)^{- \frac{1}{12}}

0.72319 \dots

Solution steps

0.3 π ((0.2)^{- 2} - 1)^{- \frac{1}{12}}

Apply exponent rule:

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

= 0.3 π \frac{1}{( 0. 2 ^{- 2} - 1 ) ^{\frac{1}{12}}}

(0. 2^{- 2} - 1)^{\frac{1}{12}} = 2 4^{\frac{1}{12}}

= 0.3 π \frac{1}{2 4 ^{\frac{1}{12}}}

Multiply fractions:

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

= 0.3 \cdot \frac{1 π}{2 4 ^{\frac{1}{12}}}

\frac{1 π}{2 4 ^{\frac{1}{12}}} = \frac{π}{1.30321 \dots}

= 0.3 \cdot \frac{π}{1.30321 \dots}

Multiply fractions:

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

= \frac{π 0.3}{1.30321 \dots}

Multiply the numbers:

3.14159 \dots \cdot 0.3 = 0.94247 \dots

= \frac{0.94247 \dots}{1.30321 \dots}

Divide the numbers:

\frac{0.94247 \dots}{1.30321 \dots} = 0.72319 \dots

= 0.72319 \dots

40 (5)^{- 0.5} (\frac{1}{25 5})^{0.2}

(5)^{65}

k^{2} (k + 2)^{2}

\frac{3 + 5}{3 - 5}

What is 0.3*pi*((0.2)^{-2}-1)^{-1/12} ?
The solution to 0.3*pi*((0.2)^{-2}-1)^{-1/12} is 0.72319…