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

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

Evaluate

$$\frac{\left(\frac{n}{p}\right)^{6}}{m^{9}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Multiply -3 times 3.

$$\frac{1}{m^{9}}n^{2\times 3}p^{-2\times 3}$$

Multiply 2 times 3.

$$\frac{1}{m^{9}}n^{6}p^{-2\times 3}$$

Multiply -2 times 3.

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

Expand

$$\frac{\left(\frac{n}{p}\right)^{6}}{m^{9}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Multiply -3 times 3.

$$\frac{1}{m^{9}}n^{2\times 3}p^{-2\times 3}$$

Multiply 2 times 3.

$$\frac{1}{m^{9}}n^{6}p^{-2\times 3}$$

Multiply -2 times 3.

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