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

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

Evaluate

$$-\frac{\left(mn\right)^{9}}{27}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

$$-\frac{1}{27}\left(m^{3}\right)^{3}\left(n^{3}\right)^{3}$$

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

$$-\frac{1}{27}m^{3\times 3}n^{3\times 3}$$

Multiply 3 times 3.

$$-\frac{1}{27}m^{9}n^{3\times 3}$$

Multiply 3 times 3.

$$-\frac{1}{27}m^{9}n^{9}$$

Expand

$$-\frac{\left(mn\right)^{9}}{27}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

$$-\frac{1}{27}\left(m^{3}\right)^{3}\left(n^{3}\right)^{3}$$

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

$$-\frac{1}{27}m^{3\times 3}n^{3\times 3}$$

Multiply 3 times 3.

$$-\frac{1}{27}m^{9}n^{3\times 3}$$

Multiply 3 times 3.

$$-\frac{1}{27}m^{9}n^{9}$$