What is 4*pi*(8.85*10^{-12})(8*10^{-2})^2*sqrt(2) ?

The solution to 4*pi*(8.85*10^{-12})(8*10^{-2})^2*sqrt(2) is 1.00658E-12

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simplify 4pi(8.8510^{-12})(810^{-2})^2*sqrt(2)

simplify

4 \cdot π \cdot (8.85 \cdot 1 0^{- 12}) (8 \cdot 1 0^{- 2})^{2} \cdot 2

1.00658 E - 12

Solution steps

4 π (8.85 \cdot 1 0^{- 12}) (8 \cdot 1 0^{- 2})^{2} 2

Apply exponent rule:

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

= 42 \cdot 8.85 π \frac{1}{1 0 ^{12}} (1 0^{- 2} \cdot 8)^{2}

(8 \cdot 1 0^{- 2})^{2} = \frac{2 ^{2}}{2 5 ^{2}}

= 42 \cdot 8.85 π \frac{1}{1 0 ^{12}} \cdot \frac{2 ^{2}}{2 5 ^{2}}

Multiply fractions:

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

= 8.85 \cdot \frac{2 ^{2} \cdot 1 \cdot 4 2 π}{1 0 ^{12} \cdot 2 5 ^{2}}

\frac{1 \cdot 2 ^{2} \cdot 4 π 2}{1 0 ^{12} \cdot 2 5 ^{2}} = \frac{π}{5 ^{16} \cdot 128 2}

= 8.85 \cdot \frac{π}{5 ^{16} \cdot 128 2}

Multiply fractions:

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

= \frac{π 8.85}{5 ^{16} \cdot 128 2}

Convert element to a decimal form

5^{16} = 152587890625

= \frac{8.85 π}{152587890625 \cdot 128 2}

Multiply the numbers:

3.14159 \dots \cdot 8.85 = 27.80309 \dots

= \frac{27.80309 \dots}{152587890625 \cdot 128 2}

Convert element to a decimal form

2 = 1.41421 \dots

= \frac{27.80309 \dots}{152587890625 \cdot 128 \cdot 1.41421 \dots}

Multiply the numbers:

152587890625 \cdot 128 \cdot 1.41421 \dots = 2.76214 E 13

= \frac{27.80309 \dots}{2.76214 E 13}

Divide the numbers:

\frac{27.80309 \dots}{2.76214 E 13} = 1.00658 E - 12

= 1.00658 E - 12

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What is 4*pi*(8.85*10^{-12})(8*10^{-2})^2*sqrt(2) ?
The solution to 4*pi*(8.85*10^{-12})(8*10^{-2})^2*sqrt(2) is 1.00658E-12