Solve (3x^2y^5)^3

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

Evaluate

$$27x^{6}y^{15}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power 3.

$$27\left(x^{2}\right)^{3}\left(y^{5}\right)^{3}$$

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

$$27x^{2\times 3}y^{5\times 3}$$

Multiply 2 times 3.

$$27x^{6}y^{5\times 3}$$

Multiply 5 times 3.

$$27x^{6}y^{15}$$

Expand

$$27x^{6}y^{15}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power 3.

$$27\left(x^{2}\right)^{3}\left(y^{5}\right)^{3}$$

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

$$27x^{2\times 3}y^{5\times 3}$$

Multiply 2 times 3.

$$27x^{6}y^{5\times 3}$$

Multiply 5 times 3.

$$27x^{6}y^{15}$$