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

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

Evaluate

$$z^{\frac{4}{3}}x^{13}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$x^{12}\left(y^{-\frac{1}{3}}\right)^{6}\left(x^{\frac{1}{2}}yz^{\frac{2}{3}}\right)^{2}$$

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

$$x^{12}y^{-2}\left(x^{\frac{1}{2}}yz^{\frac{2}{3}}\right)^{2}$$

Expand \left(x^{\frac{1}{2}}yz^{\frac{2}{3}}\right)^{2}.

$$x^{12}y^{-2}\left(x^{\frac{1}{2}}\right)^{2}y^{2}\left(z^{\frac{2}{3}}\right)^{2}$$

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

$$x^{12}y^{-2}x^{1}y^{2}\left(z^{\frac{2}{3}}\right)^{2}$$

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

$$x^{12}y^{-2}x^{1}y^{2}z^{\frac{4}{3}}$$

Calculate x to the power of 1 and get x.

$$x^{12}y^{-2}xy^{2}z^{\frac{4}{3}}$$

To multiply powers of the same base, add their exponents. Add 12 and 1 to get 13.

$$x^{13}y^{-2}y^{2}z^{\frac{4}{3}}$$

Multiply y^{-2} and y^{2} to get 1.

$$x^{13}z^{\frac{4}{3}}$$

Expand

$$z^{\frac{4}{3}}x^{13}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$x^{12}\left(y^{-\frac{1}{3}}\right)^{6}\left(x^{\frac{1}{2}}yz^{\frac{2}{3}}\right)^{2}$$

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

$$x^{12}y^{-2}\left(x^{\frac{1}{2}}yz^{\frac{2}{3}}\right)^{2}$$

Expand \left(x^{\frac{1}{2}}yz^{\frac{2}{3}}\right)^{2}.

$$x^{12}y^{-2}\left(x^{\frac{1}{2}}\right)^{2}y^{2}\left(z^{\frac{2}{3}}\right)^{2}$$

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

$$x^{12}y^{-2}x^{1}y^{2}\left(z^{\frac{2}{3}}\right)^{2}$$

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

$$x^{12}y^{-2}x^{1}y^{2}z^{\frac{4}{3}}$$

Calculate x to the power of 1 and get x.

$$x^{12}y^{-2}xy^{2}z^{\frac{4}{3}}$$

To multiply powers of the same base, add their exponents. Add 12 and 1 to get 13.

$$x^{13}y^{-2}y^{2}z^{\frac{4}{3}}$$

Multiply y^{-2} and y^{2} to get 1.

$$x^{13}z^{\frac{4}{3}}$$