Solve (2mn)^-2*(1/2m^-2n^-2)^-3=

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

Evaluate

$$2\left(mn\right)^{4}$$

Solution Steps

Expand \left(2mn\right)^{-2}.

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

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

$$\frac{1}{4}m^{-2}n^{-2}\times \left(\frac{1}{2}m^{-2}n^{-2}\right)^{-3}$$

Expand \left(\frac{1}{2}m^{-2}n^{-2}\right)^{-3}.

$$\frac{1}{4}m^{-2}n^{-2}\times \left(\frac{1}{2}\right)^{-3}\left(m^{-2}\right)^{-3}\left(n^{-2}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.

$$\frac{1}{4}m^{-2}n^{-2}\times \left(\frac{1}{2}\right)^{-3}m^{6}\left(n^{-2}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.

$$\frac{1}{4}m^{-2}n^{-2}\times \left(\frac{1}{2}\right)^{-3}m^{6}n^{6}$$

Calculate \frac{1}{2} to the power of -3 and get 8.

$$\frac{1}{4}m^{-2}n^{-2}\times 8m^{6}n^{6}$$

Multiply \frac{1}{4} and 8 to get 2.

$$2m^{-2}n^{-2}m^{6}n^{6}$$

To multiply powers of the same base, add their exponents. Add -2 and 6 to get 4.

$$2m^{4}n^{-2}n^{6}$$

To multiply powers of the same base, add their exponents. Add -2 and 6 to get 4.

$$2m^{4}n^{4}$$

Expand

$$2\left(mn\right)^{4}$$

Solution Steps

Expand \left(2mn\right)^{-2}.

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

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

$$\frac{1}{4}m^{-2}n^{-2}\times \left(\frac{1}{2}m^{-2}n^{-2}\right)^{-3}$$

Expand \left(\frac{1}{2}m^{-2}n^{-2}\right)^{-3}.

$$\frac{1}{4}m^{-2}n^{-2}\times \left(\frac{1}{2}\right)^{-3}\left(m^{-2}\right)^{-3}\left(n^{-2}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.

$$\frac{1}{4}m^{-2}n^{-2}\times \left(\frac{1}{2}\right)^{-3}m^{6}\left(n^{-2}\right)^{-3}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -3 to get 6.

$$\frac{1}{4}m^{-2}n^{-2}\times \left(\frac{1}{2}\right)^{-3}m^{6}n^{6}$$

Calculate \frac{1}{2} to the power of -3 and get 8.

$$\frac{1}{4}m^{-2}n^{-2}\times 8m^{6}n^{6}$$

Multiply \frac{1}{4} and 8 to get 2.

$$2m^{-2}n^{-2}m^{6}n^{6}$$

To multiply powers of the same base, add their exponents. Add -2 and 6 to get 4.

$$2m^{4}n^{-2}n^{6}$$

To multiply powers of the same base, add their exponents. Add -2 and 6 to get 4.

$$2m^{4}n^{4}$$