Solve (xy^{2})^2*(x^3y^5)^4

$$( x y ^ { 2 } ) ^ { 2 } * ( x ^ { 3 } y ^ { 5 } ) ^ { 4 }$$

Evaluate

$$x^{14}y^{24}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

$$x^{2}x^{3\times 4}y^{2\times 2}y^{5\times 4}$$

Multiply 3 times 4.

$$x^{2}x^{12}y^{2\times 2}y^{5\times 4}$$

Multiply 2 times 2.

$$x^{2}x^{12}y^{4}y^{5\times 4}$$

Multiply 5 times 4.

$$x^{2}x^{12}y^{4}y^{20}$$

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

$$x^{2+12}y^{4+20}$$

Add the exponents 2 and 12.

$$x^{14}y^{4+20}$$

Add the exponents 4 and 20.

$$x^{14}y^{24}$$

Expand

$$x^{14}y^{24}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Use the Commutative Property of Multiplication.

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

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

$$x^{2}x^{3\times 4}y^{2\times 2}y^{5\times 4}$$

Multiply 3 times 4.

$$x^{2}x^{12}y^{2\times 2}y^{5\times 4}$$

Multiply 2 times 2.

$$x^{2}x^{12}y^{4}y^{5\times 4}$$

Multiply 5 times 4.

$$x^{2}x^{12}y^{4}y^{20}$$

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

$$x^{2+12}y^{4+20}$$

Add the exponents 2 and 12.

$$x^{14}y^{4+20}$$

Add the exponents 4 and 20.

$$x^{14}y^{24}$$