What is 4*pi*100*10^3*22*10^{-9}*47*10^{-9} ?

The solution to 4*pi*100*10^3*22*10^{-9}*47*10^{-9} is (517pi)/(5^{13)*1024}

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simplify 4pi10010^32210^{-9}47*10^{-9}

simplify

4 \cdot π \cdot 100 \cdot 1 0^{3} \cdot 22 \cdot 1 0^{- 9} \cdot 47 \cdot 1 0^{- 9}

\frac{517 π}{5 ^{13} \cdot 1024}

Solution steps

4 π 100 \cdot 1 0^{3} \cdot 22 \cdot 1 0^{- 9} \cdot 47 \cdot 1 0^{- 9}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

1 0^{3} \cdot 1 0^{- 9} \cdot 1 0^{- 9} = 1 0^{3 - 9 - 9}

= 4 π 100 \cdot 22 \cdot 47 \cdot 1 0^{3 - 9 - 9}

Subtract the numbers:

3 - 9 - 9 = - 15

= 4 π 100 \cdot 22 \cdot 47 \cdot 1 0^{- 15}

Apply exponent rule:

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

1 0^{- 15} = \frac{1}{1 0 ^{15}}

= 4 \cdot 100 \cdot 22 \cdot 47 π \frac{1}{1 0 ^{15}}

Multiply fractions:

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

= \frac{1 \cdot 4 π 100 \cdot 22 \cdot 47}{1 0 ^{15}}

Multiply the numbers:

1 \cdot 4 \cdot 100 \cdot 22 \cdot 47 = 413600

= \frac{413600 π}{1 0 ^{15}}

Factor

413600 : 2^{5} \cdot 5^{2} \cdot 11 \cdot 47

Factor

1 0^{15} : 2^{15} \cdot 5^{15}

= \frac{2 ^{5} \cdot 5 ^{2} \cdot 11 \cdot 47 π}{2 ^{15} \cdot 5 ^{15}}

Cancel

\frac{2 ^{5} \cdot 5 ^{2} \cdot 11 \cdot 47 π}{2 ^{15} \cdot 5 ^{15}} : \frac{11 \cdot 47 π}{5 ^{13} \cdot 2 ^{10}}

= \frac{11 \cdot 47 π}{5 ^{13} \cdot 2 ^{10}}

Multiply the numbers:

11 \cdot 47 = 517

= \frac{517 π}{5 ^{13} \cdot 2 ^{10}}

2^{10} = 1024

= \frac{517 π}{5 ^{13} \cdot 1024}

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What is 4*pi*100*10^3*22*10^{-9}*47*10^{-9} ?
The solution to 4*pi*100*10^3*22*10^{-9}*47*10^{-9} is (517pi)/(5^{13)*1024}