What is 1000*10^{-6}*2pi((0.25)/2)^2 ?

The solution to 1000*10^{-6}*2pi((0.25)/2)^2 is 0.00009…

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simplify 100010^{-6}2pi((0.25)/2)^2

simplify

1000 \cdot 1 0^{- 6} \cdot 2 π (\frac{0.25}{2})^{2}

0.00009 \dots

Solution steps

1000 \cdot 1 0^{- 6} \cdot 2 π (\frac{0.25}{2})^{2}

Apply exponent rule:

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

= 1000 \cdot 2 π (\frac{0.25}{2})^{2} \frac{1}{1 0 ^{6}}

(\frac{0.25}{2})^{2} = \frac{0.2 5 ^{2}}{2 ^{2}}

= 1000 \cdot 2 π \frac{1}{1 0 ^{6}} \cdot \frac{0.2 5 ^{2}}{2 ^{2}}

Multiply fractions:

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

= \frac{1 \cdot 0.2 5 ^{2} \cdot 1000 \cdot 2 π}{1 0 ^{6} \cdot 2 ^{2}}

Multiply the numbers:

1 \cdot 1000 \cdot 2 = 2000

= \frac{2000 \cdot 0.2 5 ^{2} π}{1 0 ^{6} \cdot 2 ^{2}}

Factor

2000 : 2^{4} \cdot 5^{3}

Factor

1 0^{6} : 2^{6} \cdot 5^{6}

= \frac{2 ^{4} \cdot 5 ^{3} \cdot 0.2 5 ^{2} π}{2 ^{6} \cdot 5 ^{6} \cdot 2 ^{2}}

2^{6} \cdot 5^{6} \cdot 2^{2} = 5^{6} \cdot 2^{8}

= \frac{2 ^{4} \cdot 5 ^{3} \cdot 0.2 5 ^{2} π}{2 ^{8} \cdot 5 ^{6}}

Cancel

\frac{2 ^{4} \cdot 5 ^{3} \cdot 0.2 5 ^{2} π}{5 ^{6} \cdot 2 ^{8}} : \frac{0.2 5 ^{2} π}{2 ^{4} \cdot 5 ^{3}}

= \frac{0.2 5 ^{2} π}{2 ^{4} \cdot 5 ^{3}}

0.2 5^{2} = 0.0625

= \frac{0.0625 π}{2 ^{4} \cdot 5 ^{3}}

2^{4} \cdot 5^{3} = 2000

= \frac{0.0625 π}{2000}

Multiply the numbers:

0.0625 \cdot 3.14159 \dots = 0.19634 \dots

= \frac{0.19634 \dots}{2000}

Divide the numbers:

\frac{0.19634 \dots}{2000} = 0.00009 \dots

= 0.00009 \dots

\frac{e ^{4}}{e ^{3}}

2.5 \cdot 1 0^{- 11}

e^{- 2 l n ∣ t ∣}

e^{t} sin (t) \cdot (- 2) e^{t} sin (t)

(1 + e^{- x})^{- 1}

What is 1000*10^{-6}*2pi((0.25)/2)^2 ?
The solution to 1000*10^{-6}*2pi((0.25)/2)^2 is 0.00009…