Solve frac{(x^{2}y^{5})^{2}*(x^-1y)^-3}{x^6*y^6}

$$\frac { ( x ^ { 2 } y ^ { 5 } ) ^ { 2 } \cdot ( x ^ { - 1 } y ) ^ { - 3 } } { x ^ { 6 } \cdot y ^ { 6 } }$$

Evaluate

$$xy$$

Solution Steps

Expand \left(x^{2}y^{5}\right)^{2}.

$$\frac{\left(x^{2}\right)^{2}\left(y^{5}\right)^{2}\left(x^{-1}y\right)^{-3}}{x^{6}y^{6}}$$

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

$$\frac{x^{4}\left(y^{5}\right)^{2}\left(x^{-1}y\right)^{-3}}{x^{6}y^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{x^{4}y^{10}\left(x^{-1}y\right)^{-3}}{x^{6}y^{6}}$$

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

$$\frac{x^{4}y^{10}\left(x^{-1}\right)^{-3}y^{-3}}{x^{6}y^{6}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -3 to get 3.

$$\frac{x^{4}y^{10}x^{3}y^{-3}}{x^{6}y^{6}}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{x^{7}y^{10}y^{-3}}{x^{6}y^{6}}$$

To multiply powers of the same base, add their exponents. Add 10 and -3 to get 7.

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

Cancel out x^{6}y^{6} in both numerator and denominator.

$$xy$$

Expand

$$xy$$

Solution Steps

Expand \left(x^{2}y^{5}\right)^{2}.

$$\frac{\left(x^{2}\right)^{2}\left(y^{5}\right)^{2}\left(x^{-1}y\right)^{-3}}{x^{6}y^{6}}$$

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

$$\frac{x^{4}\left(y^{5}\right)^{2}\left(x^{-1}y\right)^{-3}}{x^{6}y^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{x^{4}y^{10}\left(x^{-1}y\right)^{-3}}{x^{6}y^{6}}$$

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

$$\frac{x^{4}y^{10}\left(x^{-1}\right)^{-3}y^{-3}}{x^{6}y^{6}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -3 to get 3.

$$\frac{x^{4}y^{10}x^{3}y^{-3}}{x^{6}y^{6}}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{x^{7}y^{10}y^{-3}}{x^{6}y^{6}}$$

To multiply powers of the same base, add their exponents. Add 10 and -3 to get 7.

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

Cancel out x^{6}y^{6} in both numerator and denominator.

$$xy$$