What is 2pi(100)(10*10^{-3}) ?

The solution to 2pi(100)(10*10^{-3}) is 2pi

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simplify 2pi(100)(10*10^{-3})

simplify

2 π (100) (10 \cdot 1 0^{- 3})

2 π

Solution steps

2 π (100) (10 \cdot 1 0^{- 3})

Apply exponent rule:

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

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

= 2 π 100 \cdot 1 0^{1 - 3}

Subtract the numbers:

1 - 3 = - 2

= 2 π 100 \cdot 1 0^{- 2}

Apply exponent rule:

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

1 0^{- 2} = \frac{1}{1 0 ^{2}}

= 2 \cdot 100 π \frac{1}{1 0 ^{2}}

Multiply fractions:

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

= \frac{1 \cdot 2 π 100}{1 0 ^{2}}

Multiply the numbers:

1 \cdot 2 \cdot 100 = 200

= \frac{200 π}{1 0 ^{2}}

Factor

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

Factor

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

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

Cancel

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

= 2 π

- 8.75 \cdot 1 0^{- 6}

2.37 \cdot 1 0^{- 13} \cdot \frac{48}{169}

7 x^{4} y^{4} (4 x^{5} y + 9 x^{2} y)