Solve frac{x^{2}(xy^{2})^3}{(x^6y^-3)^2}

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

Evaluate

$$\frac{y^{12}}{x^{7}}$$

Solution Steps

Expand \left(xy^{2}\right)^{3}.

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{x^{5}y^{6}}{\left(x^{6}y^{-3}\right)^{2}}$$

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

$$\frac{x^{5}y^{6}}{\left(x^{6}\right)^{2}\left(y^{-3}\right)^{2}}$$

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

$$\frac{x^{5}y^{6}}{x^{12}\left(y^{-3}\right)^{2}}$$

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

$$\frac{x^{5}y^{6}}{x^{12}y^{-6}}$$

Cancel out x^{5} in both numerator and denominator.

$$\frac{y^{6}}{y^{-6}x^{7}}$$

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

$$\frac{y^{12}}{x^{7}}$$

Expand

$$\frac{y^{12}}{x^{7}}$$

Solution Steps

Expand \left(xy^{2}\right)^{3}.

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{x^{5}y^{6}}{\left(x^{6}y^{-3}\right)^{2}}$$

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

$$\frac{x^{5}y^{6}}{\left(x^{6}\right)^{2}\left(y^{-3}\right)^{2}}$$

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

$$\frac{x^{5}y^{6}}{x^{12}\left(y^{-3}\right)^{2}}$$

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

$$\frac{x^{5}y^{6}}{x^{12}y^{-6}}$$

Cancel out x^{5} in both numerator and denominator.

$$\frac{y^{6}}{y^{-6}x^{7}}$$

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

$$\frac{y^{12}}{x^{7}}$$