What is ((0.2^5)/5)*4pi*9*pi*10^{-9}*2/3 ?

The solution to ((0.2^5)/5)*4pi*9*pi*10^{-9}*2/3 is 1.51597E-11

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simplify ((0.2^5)/5)4pi9*pi10^{-9}2/3

Solution

simplify

(\frac{0. 2 ^{5}}{5}) \cdot 4 π \cdot 9 \cdot π \cdot 1 0^{- 9} \cdot \frac{2}{3}

Solution

1.51597 E - 11

Solution steps

(\frac{0. 2 ^{5}}{5}) \cdot 4 π 9 π 1 0^{- 9} \cdot \frac{2}{3}

Apply exponent rule:

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

ππ = π^{1 + 1}

= \frac{0. 2 ^{5}}{5} \cdot 4 \cdot 9 π^{1 + 1} \cdot 1 0^{- 9} \cdot \frac{2}{3}

Add the numbers:

1 + 1 = 2

= \frac{0. 2 ^{5}}{5} \cdot 4 \cdot 9 π^{2} \cdot 1 0^{- 9} \cdot \frac{2}{3}

Apply exponent rule:

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

1 0^{- 9} = \frac{1}{1 0 ^{9}}

= 4 \cdot 9 π^{2} \frac{2}{3} \cdot \frac{1}{1 0 ^{9}} \cdot \frac{0. 2 ^{5}}{5}

Multiply fractions:

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

= \frac{0. 2 ^{5} \cdot 1 \cdot 2 \cdot 4 \cdot 9 π ^{2}}{5 \cdot 1 0 ^{9} \cdot 3}

Multiply the numbers:

1 \cdot 2 \cdot 4 \cdot 9 = 72

= \frac{72 \cdot 0. 2 ^{5} π ^{2}}{1 0 ^{9} \cdot 5 \cdot 3}

Multiply the numbers:

5 \cdot 3 = 15

= \frac{72 \cdot 0. 2 ^{5} π ^{2}}{1 0 ^{9} \cdot 15}

Cancel the common factor:

3

= \frac{24 \cdot 0. 2 ^{5} π ^{2}}{1 0 ^{9} \cdot 5}

Factor

24 : 2^{3} \cdot 3

Factor

1 0^{9} : 2^{9} \cdot 5^{9}

= \frac{2 ^{3} \cdot 3 \cdot 0. 2 ^{5} π ^{2}}{2 ^{9} \cdot 5 ^{9} \cdot 5}

2^{9} \cdot 5^{9} \cdot 5 = 2^{9} \cdot 5^{10}

= \frac{2 ^{3} \cdot 3 \cdot 0. 2 ^{5} π ^{2}}{5 ^{10} \cdot 2 ^{9}}

Cancel

\frac{2 ^{3} \cdot 3 \cdot 0. 2 ^{5} π ^{2}}{2 ^{9} \cdot 5 ^{10}} : \frac{3 \cdot 0. 2 ^{5} π ^{2}}{5 ^{10} \cdot 2 ^{6}}

= \frac{3 \cdot 0. 2 ^{5} π ^{2}}{5 ^{10} \cdot 2 ^{6}}

3 \cdot 0. 2^{5} π^{2} = 0.00096 π^{2}

= \frac{0.00096 π ^{2}}{5 ^{10} \cdot 2 ^{6}}

5^{10} \cdot 2^{6} = 625000000

= \frac{0.00096 π ^{2}}{625000000}

Convert element to a decimal form

π^{2} = 9.86960 \dots

= \frac{0.00096 \cdot 9.86960 \dots}{625000000}

Multiply the numbers:

0.00096 \cdot 9.86960 \dots = 0.00947 \dots

= \frac{0.00947 \dots}{625000000}

Divide the numbers:

\frac{0.00947 \dots}{625000000} = 1.51597 E - 11

= 1.51597 E - 11

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Frequently Asked Questions (FAQ)

What is ((0.2^5)/5)*4pi*9*pi*10^{-9}*2/3 ?
The solution to ((0.2^5)/5)*4pi*9*pi*10^{-9}*2/3 is 1.51597E-11

simplify ((0.2^5)/5)*4pi*9*pi*10^{-9}*2/3

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is ((0.2^5)/5)*4pi*9*pi*10^{-9}*2/3 ?

simplify ((0.2^5)/5)4pi9*pi10^{-9}2/3

What is ((0.2^5)/5)4pi9*pi10^{-9}2/3 ?