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

$$( 3 m ^ { - 2 } n ^ { 3 } ) ^ { 3 }$$

Evaluate

$$\frac{27n^{9}}{m^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power 3.

$$27\left(m^{-2}\right)^{3}\left(n^{3}\right)^{3}$$

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

$$27m^{-2\times 3}n^{3\times 3}$$

Multiply -2 times 3.

$$27\times \frac{1}{m^{6}}n^{3\times 3}$$

Multiply 3 times 3.

$$27\times \frac{1}{m^{6}}n^{9}$$

Expand

$$\frac{27n^{9}}{m^{6}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power 3.

$$27\left(m^{-2}\right)^{3}\left(n^{3}\right)^{3}$$

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

$$27m^{-2\times 3}n^{3\times 3}$$

Multiply -2 times 3.

$$27\times \frac{1}{m^{6}}n^{3\times 3}$$

Multiply 3 times 3.

$$27\times \frac{1}{m^{6}}n^{9}$$