What is 4*pi*10^{-7}*(5700)^2*0.06283*7*10^{-3} ?

The solution to 4*pi*10^{-7}*(5700)^2*0.06283*7*10^{-3} is 0.01795…

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simplify 4pi10^{-7}(5700)^20.06283710^{-3}

Solution

simplify

4 \cdot π \cdot 1 0^{- 7} \cdot (5700)^{2} \cdot 0.06283 \cdot 7 \cdot 1 0^{- 3}

Solution

0.01795 \dots

Solution steps

4 π 1 0^{- 7} (5700)^{2} \cdot 0.06283 \cdot 7 \cdot 1 0^{- 3}

Apply exponent rule:

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

1 0^{- 7} \cdot 1 0^{- 3} = 1 0^{- 7 - 3}

= 4 π 570 0^{2} \cdot 0.06283 \cdot 7 \cdot 1 0^{- 7 - 3}

Subtract the numbers:

- 7 - 3 = - 10

= 4 π 570 0^{2} \cdot 0.06283 \cdot 7 \cdot 1 0^{- 10}

Factor integer

4 = 2^{2}

= 2^{2} π 570 0^{2} \cdot 0.06283 \cdot 7 \cdot 1 0^{- 10}

Factor integer

5700 = 2^{2} \cdot 5^{2} \cdot 57

= 2^{2} π (2^{2} \cdot 5^{2} \cdot 57)^{2} \cdot 0.06283 \cdot 7 \cdot 1 0^{- 10}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(2^{2} \cdot 5^{2} \cdot 57)^{2} = (2^{2})^{2} (5^{2})^{2} \cdot 5 7^{2}

= 2^{2} π (2^{2})^{2} (5^{2})^{2} \cdot 5 7^{2} \cdot 0.06283 \cdot 7 \cdot 1 0^{- 10}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

(2^{2})^{2} = 2^{2 \cdot 2}, (5^{2})^{2} = 5^{2 \cdot 2}

= 2^{2} π 2^{2 \cdot 2} \cdot 5^{2 \cdot 2} \cdot 5 7^{2} \cdot 0.06283 \cdot 7 \cdot 1 0^{- 10}

Refine

= 2^{2} π 2^{4} \cdot 5^{4} \cdot 5 7^{2} \cdot 0.06283 \cdot 7 \cdot 1 0^{- 10}

Factor integer

10 = 2 \cdot 5

= 2^{2} π 2^{4} \cdot 5^{4} \cdot 5 7^{2} \cdot 0.06283 \cdot 7 (2 \cdot 5)^{- 10}

Apply exponent rule:

(ab)^{c} = a^{c} b^{c}

(2 \cdot 5)^{- 10} = 2^{- 10} \cdot 5^{- 10}

= 2^{2} π 2^{4} \cdot 5^{4} \cdot 5 7^{2} \cdot 0.06283 \cdot 7 \cdot 2^{- 10} \cdot 5^{- 10}

Apply exponent rule:

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

2^{2} \cdot 2^{4} \cdot 2^{- 10} = 2^{2 + 4 - 10}

= π 5^{4} \cdot 5 7^{2} \cdot 0.06283 \cdot 7 \cdot 2^{2 + 4 - 10} \cdot 5^{- 10}

Add/Subtract the numbers:

2 + 4 - 10 = - 4

= π 5^{4} \cdot 5 7^{2} \cdot 0.06283 \cdot 7 \cdot 2^{- 4} \cdot 5^{- 10}

Apply exponent rule:

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

5^{4} \cdot 5^{- 10} = 5^{4 - 10}

= π 5 7^{2} \cdot 0.06283 \cdot 7 \cdot 2^{- 4} \cdot 5^{4 - 10}

Subtract the numbers:

4 - 10 = - 6

= π 5 7^{2} \cdot 0.06283 \cdot 7 \cdot 2^{- 4} \cdot 5^{- 6}

Apply exponent rule:

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

2^{- 4} = \frac{1}{2 ^{4}}

= 5^{- 6} \cdot 5 7^{2} \cdot 7 \cdot 0.06283 π \frac{1}{2 ^{4}}

Apply exponent rule:

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

5^{- 6} = \frac{1}{5 ^{6}}

= 5 7^{2} \cdot 7 \cdot 0.06283 π \frac{1}{2 ^{4}} \cdot \frac{1}{5 ^{6}}

Multiply fractions:

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

= 0.06283 \cdot \frac{5 7 ^{2} \cdot 1 \cdot 1 \cdot 7 π}{5 ^{6} \cdot 2 ^{4}}

\frac{1 \cdot 1 π 5 7 ^{2} \cdot 7}{2 ^{4} \cdot 5 ^{6}} = \frac{22743 π}{250000}

= 0.06283 \cdot \frac{22743 π}{250000}

Multiply fractions:

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

= \frac{22743 π 0.06283}{250000}

Multiply the numbers:

22743 \cdot 0.06283 = 1428.94269

= \frac{1428.94269 π}{250000}

Multiply the numbers:

1428.94269 \cdot 3.14159 \dots = 4489.15585 \dots

= \frac{4489.15585 \dots}{250000}

Divide the numbers:

\frac{4489.15585 \dots}{250000} = 0.01795 \dots

= 0.01795 \dots

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Frequently Asked Questions (FAQ)

What is 4*pi*10^{-7}*(5700)^2*0.06283*7*10^{-3} ?
The solution to 4*pi*10^{-7}*(5700)^2*0.06283*7*10^{-3} is 0.01795…

simplify 4*pi*10^{-7}*(5700)^2*0.06283*7*10^{-3}

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 4*pi*10^{-7}*(5700)^2*0.06283*7*10^{-3} ?

simplify 4pi10^{-7}(5700)^20.06283710^{-3}

What is 4pi10^{-7}(5700)^20.06283710^{-3} ?