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simplificar 10^{1/4}40^{1/4}5^{1/2}

Solução

simplificar

1 0^{\frac{1}{4}} \cdot 4 0^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

10

Passos da solução

1 0^{\frac{1}{4}} \cdot 4 0^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

Aplicar as propriedades dos expoentes:

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

1 0^{\frac{1}{4}} \cdot 4 0^{\frac{1}{4}} = (10 \cdot 40)^{\frac{1}{4}}

= 5^{\frac{1}{2}} (10 \cdot 40)^{\frac{1}{4}}

Multiplicar os números:

10 \cdot 40 = 400

= 40 0^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

Fatorar o inteiro

400 = 5^{2} \cdot 16

= (5^{2} \cdot 16)^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

Aplicar as propriedades dos expoentes:

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

(5^{2} \cdot 16)^{\frac{1}{4}} = (5^{2})^{\frac{1}{4}} \cdot 1 6^{\frac{1}{4}}

= (5^{2})^{\frac{1}{4}} \cdot 1 6^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

Aplicar as propriedades dos expoentes:

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

(5^{2})^{\frac{1}{4}} = 5^{2 \cdot \frac{1}{4}}

= 5^{2 \cdot \frac{1}{4}} \cdot 1 6^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

Simplificar

= 5^{\frac{1}{2}} \cdot 1 6^{\frac{1}{4}} \cdot 5^{\frac{1}{2}}

Aplicar as propriedades dos expoentes:

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

5^{\frac{1}{2}} \cdot 5^{\frac{1}{2}} = 5^{\frac{1}{2} + \frac{1}{2}}

= 1 6^{\frac{1}{4}} \cdot 5^{\frac{1}{2} + \frac{1}{2}}

1 6^{\frac{1}{4}} = 2

= 2 \cdot 5^{\frac{1}{2} + \frac{1}{2}}

5^{\frac{1}{2} + \frac{1}{2}} = 5

= 2 \cdot 5

Multiplicar os números:

2 \cdot 5 = 10

= 10

s im pl i f y 0.027 \cdot 3^{- 2}

s im pl i f y (\frac{\frac{3}{125}}{2} - \frac{\frac{1}{25}}{2}) \cdot e^{- \frac{27}{1000} \cdot \frac{1}{3}}

s im pl i f y 3 x^{5} e^{- y}

s im pl i f y 0.05 \cdot 1 0^{- 2}

s im pl i f y 0.3 \cdot 1 0^{- 5}