Solve (-8y^-2/x^6y)^frac{1{3}}

$$( \frac { - 8 y ^ { - 2 } } { x ^ { 6 } y } ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$-\frac{2}{yx^{2}}$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{-8}{y^{3}x^{6}}\right)^{\frac{1}{3}}$$

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

$$\frac{\left(-8\right)^{\frac{1}{3}}}{\left(y^{3}x^{6}\right)^{\frac{1}{3}}}$$

Calculate -8 to the power of \frac{1}{3} and get -2.

$$\frac{-2}{\left(y^{3}x^{6}\right)^{\frac{1}{3}}}$$

Expand \left(y^{3}x^{6}\right)^{\frac{1}{3}}.

$$\frac{-2}{\left(y^{3}\right)^{\frac{1}{3}}\left(x^{6}\right)^{\frac{1}{3}}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and \frac{1}{3} to get 1.

$$\frac{-2}{y^{1}\left(x^{6}\right)^{\frac{1}{3}}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and \frac{1}{3} to get 2.

$$\frac{-2}{y^{1}x^{2}}$$

Calculate y to the power of 1 and get y.

$$\frac{-2}{yx^{2}}$$

Differentiate w.r.t. x

$$\frac{4}{yx^{3}}$$