pt

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Álgebra >

simplificar (16x^2)^{1/3}(\sqrt[3]{4x})

Solução

simplificar

(16 x^{2})^{\frac{1}{3}} (3 4 x)

Solução

4 x

Passos da solução

(16 x^{2})^{\frac{1}{3}} (3 4 x)

Aplique a regra:

(a) = a

(3 4 x) = 3 4 x

= (16 x^{2})^{\frac{1}{3}} 3 4 x

Simplificar

(16 x^{2})^{\frac{1}{3}} : 2 \cdot 2^{\frac{1}{3}} x^{\frac{2}{3}}

= 2 \cdot 2^{\frac{1}{3}} x^{\frac{2}{3}} 3 4 x

Simplificar

3 4 x : 34 3 x

= 2 \cdot 2^{\frac{1}{3}} x^{\frac{2}{3}} 34 3 x

Aplicar as propriedades dos radicais:

n a = a^{\frac{1}{n}}

3 x = x^{\frac{1}{3}}

= 2 \cdot 2^{\frac{1}{3}} x^{\frac{2}{3}} 34 x^{\frac{1}{3}}

Simplificar

x^{\frac{2}{3}} x^{\frac{1}{3}} : x

= 2 \cdot 2^{\frac{1}{3}} x 34

= 2 \cdot 2^{\frac{1}{3}} 34 x

2 \cdot 2^{\frac{1}{3}} = 2^{\frac{4}{3}}

= 2^{\frac{4}{3}} 34 x

Fatorar o inteiro

4 = 2^{2}

= 2^{\frac{4}{3}} 3 2^{2} x

Aplicar as propriedades dos expoentes:

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

(2^{2})^{\frac{1}{3}} = 2^{2 \cdot \frac{1}{3}}

= 2^{\frac{4}{3}} \cdot 2^{2 \cdot \frac{1}{3}} x

Simplificar

= 2^{\frac{4}{3}} \cdot 2^{\frac{2}{3}} x

Aplicar as propriedades dos expoentes:

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

2^{\frac{4}{3}} \cdot 2^{\frac{2}{3}} = 2^{\frac{4}{3} + \frac{2}{3}}

= 2^{\frac{4}{3} + \frac{2}{3}} x

2^{\frac{4}{3} + \frac{2}{3}} = 2^{2}

= 2^{2} x

2^{2} = 4

= 4 x

Exemplos populares

simplificar sqrt(pi/2)S(sqrt(2/pi)*4)

s im pl i f y \frac{π}{2} S (\frac{2}{π} \cdot 4)

simplificar 5/2 e^{-5/2}

s im pl i f y \frac{5}{2} e^{- \frac{5}{2}}

simplificar (5x^4)(3x^5)

s im pl i f y (5 x^{4}) (3 x^{5})

simplificar (-2+1)e^{-2}

s im pl i f y (- 2 + 1) e^{- 2}

simplificar sqrt(\sqrt{5)+1}*sqrt(\sqrt{5)-1}

s im pl i f y 5 + 1 \cdot 5 - 1