Solve (xy)^2/x^-5y^6

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

Evaluate

$$\frac{x^{7}}{y^{4}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Use the Commutative Property of Multiplication.

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

To raise a power to another power, multiply the exponents.

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

Multiply -5 times -1.

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

Multiply 6 times -1.

$$x^{2}x^{5}y^{2}y^{-6}$$

To multiply powers of the same base, add their exponents.

$$x^{2+5}y^{2-6}$$

Add the exponents 2 and 5.

$$x^{7}y^{2-6}$$

Add the exponents 2 and -6.

$$x^{7}y^{-4}$$

Expand

$$\frac{x^{7}}{y^{4}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Use the Commutative Property of Multiplication.

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

To raise a power to another power, multiply the exponents.

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

Multiply -5 times -1.

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

Multiply 6 times -1.

$$x^{2}x^{5}y^{2}y^{-6}$$

To multiply powers of the same base, add their exponents.

$$x^{2+5}y^{2-6}$$

Add the exponents 2 and 5.

$$x^{7}y^{2-6}$$

Add the exponents 2 and -6.

$$x^{7}y^{-4}$$