Solve (1/2x^2y^3)^3]

$$( \frac { 1 } { 2 } x ^ { 2 } y ^ { 3 } ) ^ { 3 } ]$$

Evaluate

$$\frac{x^{6}y^{9}}{8}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise \frac{1}{2} to the power 3.

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

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

$$\frac{1}{8}x^{2\times 3}y^{3\times 3}$$

Multiply 2 times 3.

$$\frac{1}{8}x^{6}y^{3\times 3}$$

Multiply 3 times 3.

$$\frac{1}{8}x^{6}y^{9}$$

Expand

$$\frac{x^{6}y^{9}}{8}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise \frac{1}{2} to the power 3.

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

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

$$\frac{1}{8}x^{2\times 3}y^{3\times 3}$$

Multiply 2 times 3.

$$\frac{1}{8}x^{6}y^{3\times 3}$$

Multiply 3 times 3.

$$\frac{1}{8}x^{6}y^{9}$$