Solve (-1/2m^3n)^3

$$( - \frac { 1 } { 2 } m ^ { 3 } n ) ^ { 3 }$$

Evaluate

$$-\frac{n^{3}m^{9}}{8}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{2}m^{3}n^{1}\right)^{3}$$

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

$$\left(-\frac{1}{2}\right)^{3}\left(m^{3}\right)^{3}\left(n^{1}\right)^{3}$$

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

$$-\frac{1}{8}\left(m^{3}\right)^{3}\left(n^{1}\right)^{3}$$

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

$$-\frac{1}{8}m^{3\times 3}n^{3}$$

Multiply 3 times 3.

$$-\frac{1}{8}m^{9}n^{3}$$

Expand

$$-\frac{n^{3}m^{9}}{8}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(-\frac{1}{2}m^{3}n^{1}\right)^{3}$$

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

$$\left(-\frac{1}{2}\right)^{3}\left(m^{3}\right)^{3}\left(n^{1}\right)^{3}$$

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

$$-\frac{1}{8}\left(m^{3}\right)^{3}\left(n^{1}\right)^{3}$$

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

$$-\frac{1}{8}m^{3\times 3}n^{3}$$

Multiply 3 times 3.

$$-\frac{1}{8}m^{9}n^{3}$$