What is 2pil^{1/2}(9.81m3^{-2})^{-1/2} ?

The solution to 2pil^{1/2}(9.81m3^{-2})^{-1/2} is 6.01820…(l/m)^{1/2}

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simplify 2pil^{1/2}(9.81m3^{-2})^{-1/2}

simplify

2 π l^{\frac{1}{2}} (9.81 m 3^{- 2})^{- \frac{1}{2}}

6.01820 \dots (\frac{l}{m})^{\frac{1}{2}}

Solution steps

2 π l^{\frac{1}{2}} (9.81 m \cdot 3^{- 2})^{- \frac{1}{2}}

Apply exponent rule:

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

= 2 π l^{\frac{1}{2}} \frac{1}{( 3 ^{- 2} \cdot 9.81 m ) ^{\frac{1}{2}}}

\frac{1}{( 9.81 m \cdot 3 ^{- 2} ) ^{\frac{1}{2}}} = \frac{1}{1.0 9 ^{\frac{1}{2}} m ^{\frac{1}{2}}}

= 2 π l^{\frac{1}{2}} \frac{1}{1.0 9 ^{\frac{1}{2}} m ^{\frac{1}{2}}}

Multiply fractions:

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

= \frac{1 \cdot 2 π l ^{\frac{1}{2}}}{1.0 9 ^{\frac{1}{2}} m ^{\frac{1}{2}}}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2 π l ^{\frac{1}{2}}}{1.0 9 ^{\frac{1}{2}} m ^{\frac{1}{2}}}

1.0 9^{\frac{1}{2}} = 1.04403 \dots

= \frac{2 π l ^{\frac{1}{2}}}{1.04403 \dots m ^{\frac{1}{2}}}

Multiply the numbers:

2 \cdot 3.14159 \dots = 6.28318 \dots

= \frac{6.28318 \dots l ^{\frac{1}{2}}}{1.04403 \dots m ^{\frac{1}{2}}}

Divide the numbers:

\frac{6.28318 \dots}{1.04403 \dots} = 6.01820 \dots

= 6.01820 \dots \cdot \frac{l ^{\frac{1}{2}}}{m ^{\frac{1}{2}}}

\frac{l ^{\frac{1}{2}}}{m ^{\frac{1}{2}}} = (\frac{l}{m})^{\frac{1}{2}}

= 6.01820 \dots (\frac{l}{m})^{\frac{1}{2}}

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What is 2pil^{1/2}(9.81m3^{-2})^{-1/2} ?
The solution to 2pil^{1/2}(9.81m3^{-2})^{-1/2} is 6.01820…(l/m)^{1/2}