Solve (mn^3*2nm^3)^-4

$$( m n ^ { 3 } \cdot 2 n m ^ { 3 } ) ^ { - 4 }$$

Evaluate

$$\frac{1}{16\left(mn\right)^{16}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(m^{4}n^{3}\times 2n\right)^{-4}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\left(m^{4}n^{4}\times 2\right)^{-4}$$

Expand \left(m^{4}n^{4}\times 2\right)^{-4}.

$$\left(m^{4}\right)^{-4}\left(n^{4}\right)^{-4}\times 2^{-4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -4 to get -16.

$$m^{-16}\left(n^{4}\right)^{-4}\times 2^{-4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -4 to get -16.

$$m^{-16}n^{-16}\times 2^{-4}$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

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

Expand

$$\frac{1}{16\left(mn\right)^{16}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(m^{4}n^{3}\times 2n\right)^{-4}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\left(m^{4}n^{4}\times 2\right)^{-4}$$

Expand \left(m^{4}n^{4}\times 2\right)^{-4}.

$$\left(m^{4}\right)^{-4}\left(n^{4}\right)^{-4}\times 2^{-4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -4 to get -16.

$$m^{-16}\left(n^{4}\right)^{-4}\times 2^{-4}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -4 to get -16.

$$m^{-16}n^{-16}\times 2^{-4}$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

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