Solve {left({x}^frac{1{6}}y^-3right)}^3

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

Evaluate

$$\frac{\sqrt{x}}{y^{9}}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$x^{\frac{1}{2}}y^{-9}$$

Expand

$$\frac{\sqrt{x}}{y^{9}}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$x^{\frac{1}{2}}y^{-9}$$