Solve -m^-1*(-2m^-3n^-3)^5

$$- m ^ { - 1 } \cdot ( - 2 m ^ { - 3 } n ^ { - 3 } ) ^ { 5 }$$

Evaluate

$$\frac{32}{n^{15}m^{16}}$$

Solution Steps

Expand \left(-2m^{-3}n^{-3}\right)^{5}.

$$\left(-m^{-1}\right)\left(-2\right)^{5}\left(m^{-3}\right)^{5}\left(n^{-3}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 5 to get -15.

$$\left(-m^{-1}\right)\left(-2\right)^{5}m^{-15}\left(n^{-3}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 5 to get -15.

$$\left(-m^{-1}\right)\left(-2\right)^{5}m^{-15}n^{-15}$$

Calculate -2 to the power of 5 and get -32.

$$\left(-m^{-1}\right)\left(-32\right)m^{-15}n^{-15}$$

Multiply -1 and -32 to get 32.

$$32m^{-1}m^{-15}n^{-15}$$

To multiply powers of the same base, add their exponents. Add -1 and -15 to get -16.

$$32m^{-16}n^{-15}$$

Expand

$$\frac{32}{n^{15}m^{16}}$$

Solution Steps

Expand \left(-2m^{-3}n^{-3}\right)^{5}.

$$\left(-m^{-1}\right)\left(-2\right)^{5}\left(m^{-3}\right)^{5}\left(n^{-3}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 5 to get -15.

$$\left(-m^{-1}\right)\left(-2\right)^{5}m^{-15}\left(n^{-3}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 5 to get -15.

$$\left(-m^{-1}\right)\left(-2\right)^{5}m^{-15}n^{-15}$$

Calculate -2 to the power of 5 and get -32.

$$\left(-m^{-1}\right)\left(-32\right)m^{-15}n^{-15}$$

Multiply -1 and -32 to get 32.

$$32m^{-1}m^{-15}n^{-15}$$

To multiply powers of the same base, add their exponents. Add -1 and -15 to get -16.

$$32m^{-16}n^{-15}$$