Solve (m^-9n^4)^-4

$$( m ^ { - 9 } n ^ { 4 } ) ^ { - 4 }$$

Evaluate

$$\frac{m^{36}}{n^{16}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(m^{-9}n^{4}\right)^{-4}$$

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

$$\left(m^{-9}\right)^{-4}\left(n^{4}\right)^{-4}$$

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

$$m^{-9\left(-4\right)}n^{4\left(-4\right)}$$

Multiply -9 times -4.

$$m^{36}n^{4\left(-4\right)}$$

Multiply 4 times -4.

$$m^{36}\times \frac{1}{n^{16}}$$

Expand

$$\frac{m^{36}}{n^{16}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(m^{-9}n^{4}\right)^{-4}$$

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

$$\left(m^{-9}\right)^{-4}\left(n^{4}\right)^{-4}$$

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

$$m^{-9\left(-4\right)}n^{4\left(-4\right)}$$

Multiply -9 times -4.

$$m^{36}n^{4\left(-4\right)}$$

Multiply 4 times -4.

$$m^{36}\times \frac{1}{n^{16}}$$