Solve (frac{2x^{-2}y^{4/3}z^-2}{x^2/3y^-2z})^-2

$$( \frac { 2 x ^ { - 2 } y ^ { 4 / 3 } z ^ { - 2 } } { x ^ { 2 / 3 } y ^ { - 2 } z } ) ^ { - 2 }$$

Evaluate

$$\frac{x^{\frac{16}{3}}z^{6}}{4y^{\frac{20}{3}}}$$

Solution Steps

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

$$\left(\frac{2x^{-2}z^{-2}y^{\frac{10}{3}}}{x^{\frac{2}{3}}z}\right)^{-2}$$

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

$$\left(\frac{2y^{\frac{10}{3}}}{x^{\frac{8}{3}}z^{3}}\right)^{-2}$$

To raise \frac{2y^{\frac{10}{3}}}{x^{\frac{8}{3}}z^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2y^{\frac{10}{3}}\right)^{-2}}{\left(x^{\frac{8}{3}}z^{3}\right)^{-2}}$$

Expand \left(2y^{\frac{10}{3}}\right)^{-2}.

$$\frac{2^{-2}\left(y^{\frac{10}{3}}\right)^{-2}}{\left(x^{\frac{8}{3}}z^{3}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{10}{3} and -2 to get -\frac{20}{3}.

$$\frac{2^{-2}y^{-\frac{20}{3}}}{\left(x^{\frac{8}{3}}z^{3}\right)^{-2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}y^{-\frac{20}{3}}}{\left(x^{\frac{8}{3}}z^{3}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}y^{-\frac{20}{3}}}{\left(x^{\frac{8}{3}}\right)^{-2}\left(z^{3}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{8}{3} and -2 to get -\frac{16}{3}.

$$\frac{\frac{1}{4}y^{-\frac{20}{3}}}{x^{-\frac{16}{3}}\left(z^{3}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{\frac{1}{4}y^{-\frac{20}{3}}}{x^{-\frac{16}{3}}z^{-6}}$$

Expand

$$\frac{x^{\frac{16}{3}}z^{6}}{4y^{\frac{20}{3}}}$$

Solution Steps

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

$$\left(\frac{2x^{-2}z^{-2}y^{\frac{10}{3}}}{x^{\frac{2}{3}}z}\right)^{-2}$$

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

$$\left(\frac{2y^{\frac{10}{3}}}{x^{\frac{8}{3}}z^{3}}\right)^{-2}$$

To raise \frac{2y^{\frac{10}{3}}}{x^{\frac{8}{3}}z^{3}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2y^{\frac{10}{3}}\right)^{-2}}{\left(x^{\frac{8}{3}}z^{3}\right)^{-2}}$$

Expand \left(2y^{\frac{10}{3}}\right)^{-2}.

$$\frac{2^{-2}\left(y^{\frac{10}{3}}\right)^{-2}}{\left(x^{\frac{8}{3}}z^{3}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{10}{3} and -2 to get -\frac{20}{3}.

$$\frac{2^{-2}y^{-\frac{20}{3}}}{\left(x^{\frac{8}{3}}z^{3}\right)^{-2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}y^{-\frac{20}{3}}}{\left(x^{\frac{8}{3}}z^{3}\right)^{-2}}$$

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

$$\frac{\frac{1}{4}y^{-\frac{20}{3}}}{\left(x^{\frac{8}{3}}\right)^{-2}\left(z^{3}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{8}{3} and -2 to get -\frac{16}{3}.

$$\frac{\frac{1}{4}y^{-\frac{20}{3}}}{x^{-\frac{16}{3}}\left(z^{3}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{\frac{1}{4}y^{-\frac{20}{3}}}{x^{-\frac{16}{3}}z^{-6}}$$