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

Solução

simplificar

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

1.51597 E - 11

Passos da solução

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

Aplicar as propriedades dos expoentes:

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}

Somar:

1 + 1 = 2

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

Aplicar as propriedades dos expoentes:

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}

Multiplicar frações:

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}

Multiplicar os números:

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

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

Multiplicar os números:

5 \cdot 3 = 15

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

Eliminar o fator comum:

3

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

Fatorar

24 : 2^{3} \cdot 3

Fatorar

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}}

Cancelar

\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}

Converter o elemento em uma forma decimal

π^{2} = 9.86960 \dots

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

Multiplicar os números:

0.00096 \cdot 9.86960 \dots = 0.00947 \dots

= \frac{0.00947 \dots}{625000000}

Dividir:

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

= 1.51597 E - 11

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