What is 2pi(10)100*10^{-6} ?

The solution to 2pi(10)100*10^{-6} is pi/(500)

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simplify 2pi(10)100*10^{-6}

simplify

2 π (10) 100 \cdot 1 0^{- 6}

\frac{π}{500}

Decimal Notation

0.00628 \dots

Solution steps

2 π (10) \cdot 100 \cdot 1 0^{- 6}

Apply exponent rule:

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

10 \cdot 1 0^{- 6} = 1 0^{1 - 6}

= 2 π 100 \cdot 1 0^{1 - 6}

Subtract the numbers:

1 - 6 = - 5

= 2 π 100 \cdot 1 0^{- 5}

Apply exponent rule:

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

1 0^{- 5} = \frac{1}{1 0 ^{5}}

= 2 \cdot 100 π \frac{1}{1 0 ^{5}}

Multiply fractions:

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

= \frac{1 \cdot 2 π 100}{1 0 ^{5}}

Multiply the numbers:

1 \cdot 2 \cdot 100 = 200

= \frac{200 π}{1 0 ^{5}}

Factor

200 : 2^{3} \cdot 5^{2}

Factor

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

= \frac{2 ^{3} \cdot 5 ^{2} π}{2 ^{5} \cdot 5 ^{5}}

Cancel

\frac{2 ^{3} \cdot 5 ^{2} π}{2 ^{5} \cdot 5 ^{5}} : \frac{π}{5 ^{3} \cdot 2 ^{2}}

= \frac{π}{5 ^{3} \cdot 2 ^{2}}

5^{3} \cdot 2^{2} = 500

= \frac{π}{500}

13.612 \cdot 1 0^{- 3} (0.5) (100 0^{2} - 35 0^{2})

(\frac{1}{2} a^{2} b^{5}) (\frac{3}{8} a^{4} b c^{2})

\frac{x + 2}{x}

\frac{1296 x ^{8} - 72 x ^{4} + 1}{144 x ^{4}}