Solve frac{(xy^{2}z^{-2})^4}{(x^3y^-1z^3)}

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

Evaluate

$$\frac{xy^{9}}{z^{11}}$$

Solution Steps

Expand \left(xy^{2}z^{-2}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

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

To raise a power to another power, multiply the exponents. Multiply -2 and 4 to get -8.

$$\frac{x^{4}y^{8}z^{-8}}{x^{3}y^{-1}z^{3}}$$

Cancel out x^{3} in both numerator and denominator.

$$\frac{z^{-8}xy^{8}}{\frac{1}{y}z^{3}}$$

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

$$\frac{z^{-8}xy^{9}}{z^{3}}$$

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

$$\frac{xy^{9}}{z^{11}}$$

Expand

$$\frac{xy^{9}}{z^{11}}$$

Solution Steps

Expand \left(xy^{2}z^{-2}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

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

To raise a power to another power, multiply the exponents. Multiply -2 and 4 to get -8.

$$\frac{x^{4}y^{8}z^{-8}}{x^{3}y^{-1}z^{3}}$$

Cancel out x^{3} in both numerator and denominator.

$$\frac{z^{-8}xy^{8}}{\frac{1}{y}z^{3}}$$

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

$$\frac{z^{-8}xy^{9}}{z^{3}}$$

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

$$\frac{xy^{9}}{z^{11}}$$