Solve (1/2a^2x^3)^3

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

Evaluate

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

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

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

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

Multiply 2 times 3.

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

Multiply 3 times 3.

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

Expand

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

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

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

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

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

Multiply 2 times 3.

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

Multiply 3 times 3.

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