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simplificar 1/2 (8.8510^{-12})(4500)^210^6

Solución

simplificar

\frac{1}{2} (8.85 \cdot 1 0^{- 12}) (4500)^{2} \cdot 1 0^{6}

89.60625

Pasos de solución

\frac{1}{2} (8.85 \cdot 1 0^{- 12}) (4500)^{2} \cdot 1 0^{6}

Aplicar las leyes de los exponentes:

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

= 1 0^{6} \cdot 450 0^{2} \cdot 8.85 \cdot \frac{1}{2} \cdot \frac{1}{1 0 ^{12}}

Factorizar entero

4500 = 5^{3} \cdot 2^{2} \cdot 9

= \frac{1}{2} \cdot 8.85 \cdot \frac{1}{1 0 ^{12}} (2^{2} \cdot 5^{3} \cdot 9)^{2} \cdot 1 0^{6}

Aplicar las leyes de los exponentes:

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

(2^{2} \cdot 5^{3} \cdot 9)^{2} = (2^{2})^{2} (5^{3})^{2} \cdot 9^{2}

= \frac{1}{2} \cdot 8.85 \cdot \frac{1}{1 0 ^{12}} (2^{2})^{2} (5^{3})^{2} \cdot 9^{2} \cdot 1 0^{6}

Aplicar las leyes de los exponentes:

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

(2^{2})^{2} = 2^{2 \cdot 2}, (5^{3})^{2} = 5^{3 \cdot 2}

= \frac{1}{2} \cdot 8.85 \cdot \frac{1}{1 0 ^{12}} \cdot 2^{2 \cdot 2} \cdot 5^{3 \cdot 2} \cdot 9^{2} \cdot 1 0^{6}

Simplificar

= \frac{1}{2} \cdot 8.85 \cdot \frac{1}{1 0 ^{12}} \cdot 2^{4} \cdot 5^{6} \cdot 9^{2} \cdot 1 0^{6}

Factorizar entero

10 = 2 \cdot 5

= \frac{1}{2} \cdot 8.85 \cdot \frac{1}{1 0 ^{12}} \cdot 2^{4} \cdot 5^{6} \cdot 9^{2} (2 \cdot 5)^{6}

Aplicar las leyes de los exponentes:

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

(2 \cdot 5)^{6} = 2^{6} \cdot 5^{6}

= \frac{1}{2} \cdot 8.85 \cdot \frac{1}{1 0 ^{12}} \cdot 2^{4} \cdot 5^{6} \cdot 9^{2} \cdot 2^{6} \cdot 5^{6}

Aplicar las leyes de los exponentes:

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

2^{4} \cdot 2^{6} = 2^{4 + 6}

= \frac{1}{2} \cdot 8.85 \cdot \frac{1}{1 0 ^{12}} \cdot 5^{6} \cdot 9^{2} \cdot 2^{4 + 6} \cdot 5^{6}

Sumar:

4 + 6 = 10

= \frac{1}{2} \cdot 8.85 \cdot \frac{1}{1 0 ^{12}} \cdot 5^{6} \cdot 9^{2} \cdot 2^{10} \cdot 5^{6}

Aplicar las leyes de los exponentes:

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

5^{6} \cdot 5^{6} = 5^{6 + 6}

= \frac{1}{2} \cdot 8.85 \cdot \frac{1}{1 0 ^{12}} \cdot 9^{2} \cdot 2^{10} \cdot 5^{6 + 6}

Sumar:

6 + 6 = 12

= \frac{1}{2} \cdot 8.85 \cdot \frac{1}{1 0 ^{12}} \cdot 9^{2} \cdot 2^{10} \cdot 5^{12}

Multiplicar fracciones:

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

= 8.85 \cdot \frac{5 ^{12} \cdot 2 ^{10} \cdot 9 ^{2} \cdot 1 \cdot 1}{1 0 ^{12} \cdot 2}

\frac{1 \cdot 1 \cdot 9 ^{2} \cdot 2 ^{10} \cdot 5 ^{12}}{2 \cdot 1 0 ^{12}} = \frac{81}{8}

= 8.85 \cdot \frac{81}{8}

Multiplicar fracciones:

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

= \frac{81 \cdot 8.85}{8}

Multiplicar los numeros:

81 \cdot 8.85 = 716.85

= \frac{716.85}{8}

Dividir:

\frac{716.85}{8} = 89.60625

= 89.60625

e^{- 3094}

1 0^{- 10} \cdot 1500 \cdot 6.21

20 e^{- 2}