Esercizio
$\left(\sqrt[3]{\frac{-8x^6}{y-8}}\right)^2\left(\sqrt[5]{\frac{x^3y^{-10}}{32x^8}}\right)^3$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. ((-8x^6)/(y-8))^(1/3)^2((x^3y^(-10))/(32x^8))^(1/5)^3. Simplify \left(\sqrt[3]{\frac{-8x^6}{y-8}}\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{3} and n equals 2. Simplify \left(\sqrt[5]{\frac{x^3y^{-10}}{32x^8}}\right)^3 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{5} and n equals 3. Applicare la formula: \frac{a^m}{a^n}=\frac{1}{a^{\left(n-m\right)}}, dove a=x, m=3 e n=8. Applicare la formula: \frac{x^a}{b}=\frac{1}{bx^{-a}}, dove a=-10, b=32x^{5} e x=y.
((-8x^6)/(y-8))^(1/3)^2((x^3y^(-10))/(32x^8))^(1/5)^3
Risposta finale al problema
$\frac{\sqrt[3]{\left(-8x^6\right)^{2}}}{8\sqrt[3]{\left(y-8\right)^{2}}x^{3}y^{6}}$