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

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

Evaluate

$$\frac{y^{11}}{x^{6}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply -2 times 2.

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

Multiply 2 times -1.

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

Multiply 4 times 2.

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

Multiply -3 times -1.

$$x^{-4}x^{-2}y^{8}y^{3}$$

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

$$x^{-4-2}y^{8+3}$$

Add the exponents -4 and -2.

$$x^{-6}y^{8+3}$$

Add the exponents 8 and 3.

$$x^{-6}y^{11}$$

Expand

$$\frac{y^{11}}{x^{6}}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

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

Multiply -2 times 2.

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

Multiply 2 times -1.

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

Multiply 4 times 2.

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

Multiply -3 times -1.

$$x^{-4}x^{-2}y^{8}y^{3}$$

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

$$x^{-4-2}y^{8+3}$$

Add the exponents -4 and -2.

$$x^{-6}y^{8+3}$$

Add the exponents 8 and 3.

$$x^{-6}y^{11}$$