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Popular >

simplificar (360^{30}1000^{50})/(48^{60)625^{45}}

Solución

simplificar

\frac{36 0 ^{30} \cdot 100 0 ^{50}}{4 8 ^{60} \cdot 62 5 ^{45}}

Solución

1

Pasos de solución

\frac{36 0 ^{30} \cdot 100 0 ^{50}}{4 8 ^{60} \cdot 62 5 ^{45}}

Factorizar

36 0^{30} : 2 4^{30} \cdot 1 5^{30}

= \frac{2 4 ^{30} \cdot 1 5 ^{30} \cdot 100 0 ^{50}}{4 8 ^{60} \cdot 62 5 ^{45}}

Factorizar

4 8^{60} : 2 4^{60} \cdot 2^{60}

= \frac{2 4 ^{30} \cdot 1 5 ^{30} \cdot 100 0 ^{50}}{2 4 ^{60} \cdot 2 ^{60} \cdot 62 5 ^{45}}

\frac{2 4 ^{30}}{2 4 ^{60}} = \frac{1}{2 4 ^{30}}

= \frac{1 5 ^{30} \cdot 100 0 ^{50}}{2 4 ^{30} \cdot 2 ^{60} \cdot 62 5 ^{45}}

Factorizar

1 5^{30} : 3^{30} \cdot 5^{30}

= \frac{3 ^{30} \cdot 5 ^{30} \cdot 100 0 ^{50}}{2 4 ^{30} \cdot 2 ^{60} \cdot 62 5 ^{45}}

Factorizar

2 4^{30} : 3^{30} \cdot 8^{30}

= \frac{3 ^{30} \cdot 5 ^{30} \cdot 100 0 ^{50}}{3 ^{30} \cdot 8 ^{30} \cdot 2 ^{60} \cdot 62 5 ^{45}}

Eliminar los terminos comunes:

3^{30}

= \frac{5 ^{30} \cdot 100 0 ^{50}}{8 ^{30} \cdot 2 ^{60} \cdot 62 5 ^{45}}

Factorizar

62 5^{45} : 5^{180}

= \frac{5 ^{30} \cdot 100 0 ^{50}}{8 ^{30} \cdot 2 ^{60} \cdot 5 ^{180}}

\frac{5 ^{30}}{5 ^{180}} = \frac{1}{5 ^{150}}

= \frac{100 0 ^{50}}{8 ^{30} \cdot 2 ^{60} \cdot 5 ^{150}}

Factorizar

100 0^{50} : 8^{50} \cdot 12 5^{50}

= \frac{8 ^{50} \cdot 12 5 ^{50}}{8 ^{30} \cdot 2 ^{60} \cdot 5 ^{150}}

\frac{8 ^{50}}{8 ^{30}} = 8^{20}

= \frac{8 ^{20} \cdot 12 5 ^{50}}{2 ^{60} \cdot 5 ^{150}}

Factorizar

8^{20} : 2^{60}

= \frac{2 ^{60} \cdot 12 5 ^{50}}{2 ^{60} \cdot 5 ^{150}}

Eliminar los terminos comunes:

2^{60}

= \frac{12 5 ^{50}}{5 ^{150}}

Factorizar

12 5^{50} : 5^{150}

= \frac{5 ^{150}}{5 ^{150}}

Aplicar las propiedades de las fracciones:

\frac{a}{a} = 1

= 1

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