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Popular >

simplify 10^{-7}4pi40^2

Solution

simplify

1 0^{- 7} \cdot 4 π \cdot 4 0^{2}

Solution

\frac{2 π}{3125}

+1

Decimal Notation

0.00201 \dots

Solution steps

1 0^{- 7} \cdot 4 π 4 0^{2}

Apply exponent rule:

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

= 4 0^{2} \cdot 4 π \frac{1}{1 0 ^{7}}

Multiply fractions:

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

= \frac{1 \cdot 4 π 4 0 ^{2}}{1 0 ^{7}}

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4 0 ^{2} \cdot 4 π}{1 0 ^{7}}

Factor

4 0^{2} : 2^{6} \cdot 5^{2}

Factor

1 0^{7} : 2^{7} \cdot 5^{7}

Factor

4 : 2^{2}

= \frac{2 ^{6} \cdot 2 ^{2} \cdot 5 ^{2} π}{2 ^{7} \cdot 5 ^{7}}

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

= \frac{2 ^{8} \cdot 5 ^{2} π}{2 ^{7} \cdot 5 ^{7}}

Cancel

\frac{π 2 ^{8} \cdot 5 ^{2}}{2 ^{7} \cdot 5 ^{7}} : \frac{2 π}{5 ^{5}}

= \frac{2 π}{5 ^{5}}

5^{5} = 3125

= \frac{2 π}{3125}

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Frequently Asked Questions (FAQ)

What is 10^{-7}*4pi*40^2 ?
The solution to 10^{-7}*4pi*40^2 is (2pi)/(3125)