Solve (m^-3/(2n)^-4)^-2

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

Evaluate

$$\frac{m^{6}}{256n^{8}}$$

Solution Steps

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

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

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

$$\left(\frac{m^{-3}}{\frac{1}{16}n^{-4}}\right)^{-2}$$

To raise \frac{m^{-3}}{\frac{1}{16}n^{-4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(m^{-3}\right)^{-2}}{\left(\frac{1}{16}n^{-4}\right)^{-2}}$$

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

$$\frac{m^{6}}{\left(\frac{1}{16}n^{-4}\right)^{-2}}$$

Expand \left(\frac{1}{16}n^{-4}\right)^{-2}.

$$\frac{m^{6}}{\left(\frac{1}{16}\right)^{-2}\left(n^{-4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -2 to get 8.

$$\frac{m^{6}}{\left(\frac{1}{16}\right)^{-2}n^{8}}$$

Calculate \frac{1}{16} to the power of -2 and get 256.

$$\frac{m^{6}}{256n^{8}}$$

Expand

$$\frac{m^{6}}{256n^{8}}$$

Solution Steps

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

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

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

$$\left(\frac{m^{-3}}{\frac{1}{16}n^{-4}}\right)^{-2}$$

To raise \frac{m^{-3}}{\frac{1}{16}n^{-4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(m^{-3}\right)^{-2}}{\left(\frac{1}{16}n^{-4}\right)^{-2}}$$

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

$$\frac{m^{6}}{\left(\frac{1}{16}n^{-4}\right)^{-2}}$$

Expand \left(\frac{1}{16}n^{-4}\right)^{-2}.

$$\frac{m^{6}}{\left(\frac{1}{16}\right)^{-2}\left(n^{-4}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -2 to get 8.

$$\frac{m^{6}}{\left(\frac{1}{16}\right)^{-2}n^{8}}$$

Calculate \frac{1}{16} to the power of -2 and get 256.

$$\frac{m^{6}}{256n^{8}}$$