Solve frac{(2pm^{-1}q^0)^-4*2m^-1p^3}{2m-2}

$$\frac { ( 2 p m ^ { - 1 } q ^ { 0 } ) ^ { - 4 } \times 2 m ^ { - 1 } p ^ { 3 } } { 2 m - 2 }$$

Evaluate

$$\frac{m^{3}}{16p\left(m-1\right)}$$

Short Solution Steps

Calculate q to the power of 0 and get 1.

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

Multiply 2 and 1 to get 2.

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

Expand \left(2pm^{-1}\right)^{-4}.

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

To raise a power to another power, multiply the exponents. Multiply -1 and -4 to get 4.

$$\frac{2^{-4}p^{-4}m^{4}\times 2m^{-1}p^{3}}{2m-2}$$

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

$$\frac{\frac{1}{16}p^{-4}m^{4}\times 2m^{-1}p^{3}}{2m-2}$$

Multiply \frac{1}{16} and 2 to get \frac{1}{8}.

$$\frac{\frac{1}{8}p^{-4}m^{4}m^{-1}p^{3}}{2m-2}$$

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

$$\frac{\frac{1}{8}p^{-4}m^{3}p^{3}}{2m-2}$$

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

$$\frac{\frac{1}{8}p^{-1}m^{3}}{2m-2}$$

Expand

$$\frac{m^{3}}{16p\left(m-1\right)}$$

Short Solution Steps

Calculate q to the power of 0 and get 1.

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

Multiply 2 and 1 to get 2.

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

Expand \left(2pm^{-1}\right)^{-4}.

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

To raise a power to another power, multiply the exponents. Multiply -1 and -4 to get 4.

$$\frac{2^{-4}p^{-4}m^{4}\times 2m^{-1}p^{3}}{2m-2}$$

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

$$\frac{\frac{1}{16}p^{-4}m^{4}\times 2m^{-1}p^{3}}{2m-2}$$

Multiply \frac{1}{16} and 2 to get \frac{1}{8}.

$$\frac{\frac{1}{8}p^{-4}m^{4}m^{-1}p^{3}}{2m-2}$$

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

$$\frac{\frac{1}{8}p^{-4}m^{3}p^{3}}{2m-2}$$

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

$$\frac{\frac{1}{8}p^{-1}m^{3}}{2m-2}$$