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simplificar (1/3 a^3b^2c)(2/5 a^4bc^2)(6ac)(10/3 a^4b^2)

Solución

simplificar

(\frac{1}{3} a^{3} b^{2} c) (\frac{2}{5} a^{4} b c^{2}) (6 a c) (\frac{10}{3} a^{4} b^{2})

\frac{8 a ^{12} b ^{5} c ^{4}}{3}

Pasos de solución

(\frac{1}{3} a^{3} b^{2} c) (\frac{2}{5} a^{4} b c^{2}) (6 a c) (\frac{10}{3} a^{4} b^{2})

Aplicar las leyes de los exponentes:

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

a^{3} a^{4} a a^{4} = a^{3 + 4 + 1 + 4}

= \frac{1}{3} b^{2} c \frac{2}{5} b c^{2} \cdot 6 c \frac{10}{3} a^{3 + 4 + 1 + 4} b^{2}

Sumar:

3 + 4 + 1 + 4 = 12

= \frac{1}{3} b^{2} c \frac{2}{5} b c^{2} \cdot 6 c \frac{10}{3} a^{12} b^{2}

Aplicar las leyes de los exponentes:

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

b^{2} b b^{2} = b^{2 + 1 + 2}

= \frac{1}{3} c \frac{2}{5} c^{2} \cdot 6 c \frac{10}{3} a^{12} b^{2 + 1 + 2}

Sumar:

2 + 1 + 2 = 5

= \frac{1}{3} c \frac{2}{5} c^{2} \cdot 6 c \frac{10}{3} a^{12} b^{5}

Aplicar las leyes de los exponentes:

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

c c^{2} c = c^{1 + 2 + 1}

= \frac{1}{3} \cdot \frac{2}{5} \cdot 6 c^{1 + 2 + 1} \frac{10}{3} a^{12} b^{5}

Sumar:

1 + 2 + 1 = 4

= \frac{1}{3} \cdot \frac{2}{5} \cdot 6 c^{4} \frac{10}{3} a^{12} b^{5}

Multiplicar fracciones:

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

= \frac{1 \cdot 2 \cdot 10 \cdot 6 c ^{4} a ^{12} b ^{5}}{3 \cdot 5 \cdot 3}

Simplificar

= \frac{120 a ^{12} b ^{5} c ^{4}}{45}

Eliminar los terminos comunes:

15

= \frac{8 a ^{12} b ^{5} c ^{4}}{3}

0.177 \cdot 1 0^{- 4} (1) \frac{0.06 - 0.001}{0.001}

0.37 (5187368.42105)^{- \frac{1}{5}} (8)

5.29 \cdot 1 0^{- 6}

8.2 x 1 0^{- 5}

(1.8 \cdot 1 0^{12}) (1.6 \cdot 1 0^{- 19})