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Popular Álgebra >

simplificar 1/2 (5*10^{-2})(2pi^{60})^2(0.06)^2(40)

Solución

simplificar

\frac{1}{2} (5 \cdot 1 0^{- 2}) (2 π^{60})^{2} (0.06)^{2} (40)

Solución

6.5516 E 57

Pasos de solución

\frac{1}{2} (5 \cdot 1 0^{- 2}) (2 π^{60})^{2} (0.06)^{2} (40)

Aplicar las leyes de los exponentes:

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

= 5 \cdot 40 \cdot 0.0 6^{2} \cdot \frac{1}{2} \cdot \frac{1}{1 0 ^{2}} (2 π^{60})^{2}

(2 π^{60})^{2} = 2^{2} π^{120}

= 2^{2} \cdot 5 \cdot 40 \cdot 0.0 6^{2} π^{120} \frac{1}{2} \cdot \frac{1}{1 0 ^{2}}

Multiplicar fracciones:

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

= \frac{1 \cdot 1 \cdot 5 \cdot 2 ^{2} π ^{120} \cdot 0.0 6 ^{2} \cdot 40}{2 \cdot 1 0 ^{2}}

Multiplicar los numeros:

1 \cdot 1 \cdot 5 \cdot 40 = 200

= \frac{2 ^{2} \cdot 200 \cdot 0.0 6 ^{2} π ^{120}}{1 0 ^{2} \cdot 2}

Dividir:

\frac{200}{2} = 100

= \frac{2 ^{2} \cdot 100 \cdot 0.0 6 ^{2} π ^{120}}{1 0 ^{2}}

Factorizar

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

Factorizar

100 : 2^{2} \cdot 5^{2}

= \frac{2 ^{2} \cdot 2 ^{2} \cdot 5 ^{2} \cdot 0.0 6 ^{2} π ^{120}}{2 ^{2} \cdot 5 ^{2}}

2^{2} \cdot 2^{2} \cdot 5^{2} \cdot 0.0 6^{2} π^{120} = 2^{4} \cdot 5^{2} \cdot 0.0 6^{2} π^{120}

= \frac{2 ^{4} \cdot 5 ^{2} \cdot 0.0 6 ^{2} π ^{120}}{2 ^{2} \cdot 5 ^{2}}

Cancelar

\frac{2 ^{4} \cdot 5 ^{2} \cdot 0.0 6 ^{2} π ^{120}}{2 ^{2} \cdot 5 ^{2}} : 2^{2} \cdot 0.0 6^{2} π^{120}

= 2^{2} \cdot 0.0 6^{2} π^{120}

2^{2} = 4

= 4 \cdot 0.0 6^{2} π^{120}

0.0 6^{2} = 0.0036

= 4 \cdot 0.0036 π^{120}

Convertir el elemento a una forma decimal

π^{120} = 4.54972 E 59

= 4 \cdot 0.0036 \cdot 4.54972 E 59

Multiplicar los numeros:

4 \cdot 0.0036 \cdot 4.54972 E 59 = 6.5516 E 57

= 6.5516 E 57

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