Solve (-8x^3/y^-6)^2/3

$$( \frac { - 8 x ^ { 3 } } { y ^ { - 6 } } ) ^ { 2 / 3 }$$

Evaluate

$$4x^{2}y^{4}$$

Solution Steps

To raise \frac{-8x^{3}}{y^{-6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(-8x^{3}\right)^{\frac{2}{3}}}{\left(y^{-6}\right)^{\frac{2}{3}}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and \frac{2}{3} to get -4.

$$\frac{\left(-8x^{3}\right)^{\frac{2}{3}}}{y^{-4}}$$

Expand \left(-8x^{3}\right)^{\frac{2}{3}}.

$$\frac{\left(-8\right)^{\frac{2}{3}}\left(x^{3}\right)^{\frac{2}{3}}}{y^{-4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and \frac{2}{3} to get 2.

$$\frac{\left(-8\right)^{\frac{2}{3}}x^{2}}{y^{-4}}$$

Calculate -8 to the power of \frac{2}{3} and get 4.

$$\frac{4x^{2}}{y^{-4}}$$

Differentiate w.r.t. x

$$8xy^{4}$$