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Popular Álgebra >

simplificar 4pi696340000^2567810^{-8}

Solução

simplificar

4 \cdot π \cdot 69634000 0^{2} \cdot 5678 \cdot 1 0^{- 8}

Solução

\frac{69634000 0 ^{2} \cdot 2839 π}{12500000}

+1

Decimal

3.45978 E 14

Passos da solução

4 π 69634000 0^{2} \cdot 5678 \cdot 1 0^{- 8}

Aplicar as propriedades dos expoentes:

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

= 69634000 0^{2} \cdot 4 \cdot 5678 π \frac{1}{1 0 ^{8}}

Multiplicar frações:

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

= \frac{1 \cdot 4 π 69634000 0 ^{2} \cdot 5678}{1 0 ^{8}}

Multiplicar os números:

1 \cdot 4 \cdot 5678 = 22712

= \frac{69634000 0 ^{2} \cdot 22712 π}{1 0 ^{8}}

Fatorar

22712 : 2^{3} \cdot 17 \cdot 167

Fatorar

1 0^{8} : 2^{8} \cdot 5^{8}

= \frac{2 ^{3} \cdot 69634000 0 ^{2} \cdot 17 \cdot 167 π}{2 ^{8} \cdot 5 ^{8}}

Cancelar

\frac{2 ^{3} \cdot 17 \cdot 167 π 69634000 0 ^{2}}{2 ^{8} \cdot 5 ^{8}} : \frac{69634000 0 ^{2} \cdot 17 \cdot 167 π}{5 ^{8} \cdot 2 ^{5}}

= \frac{69634000 0 ^{2} \cdot 17 \cdot 167 π}{5 ^{8} \cdot 2 ^{5}}

Multiplicar os números:

17 \cdot 167 = 2839

= \frac{69634000 0 ^{2} \cdot 2839 π}{5 ^{8} \cdot 2 ^{5}}

5^{8} \cdot 2^{5} = 12500000

= \frac{69634000 0 ^{2} \cdot 2839 π}{12500000}

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