Solve (2x^1/2/z^-1/6y^2/3)^6

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

Evaluate

$$\frac{64zx^{3}}{y^{4}}$$

Solution Steps

To raise \frac{2x^{\frac{1}{2}}}{z^{-\frac{1}{6}}y^{\frac{2}{3}}} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(2x^{\frac{1}{2}}\right)^{6}.

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

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

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

Calculate 2 to the power of 6 and get 64.

$$\frac{64x^{3}}{\left(z^{-\frac{1}{6}}y^{\frac{2}{3}}\right)^{6}}$$

Expand \left(z^{-\frac{1}{6}}y^{\frac{2}{3}}\right)^{6}.

$$\frac{64x^{3}}{\left(z^{-\frac{1}{6}}\right)^{6}\left(y^{\frac{2}{3}}\right)^{6}}$$

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

$$\frac{64x^{3}}{z^{-1}\left(y^{\frac{2}{3}}\right)^{6}}$$

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

$$\frac{64x^{3}}{z^{-1}y^{4}}$$

Expand

$$\frac{64zx^{3}}{y^{4}}$$

Solution Steps

To raise \frac{2x^{\frac{1}{2}}}{z^{-\frac{1}{6}}y^{\frac{2}{3}}} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(2x^{\frac{1}{2}}\right)^{6}.

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

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

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

Calculate 2 to the power of 6 and get 64.

$$\frac{64x^{3}}{\left(z^{-\frac{1}{6}}y^{\frac{2}{3}}\right)^{6}}$$

Expand \left(z^{-\frac{1}{6}}y^{\frac{2}{3}}\right)^{6}.

$$\frac{64x^{3}}{\left(z^{-\frac{1}{6}}\right)^{6}\left(y^{\frac{2}{3}}\right)^{6}}$$

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

$$\frac{64x^{3}}{z^{-1}\left(y^{\frac{2}{3}}\right)^{6}}$$

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

$$\frac{64x^{3}}{z^{-1}y^{4}}$$