Solve (frac{mn^{-2}p}{m^{2}np^{4}})^{-2}(mn^-2p/m^2np^4)^3

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

Evaluate

$$\frac{1}{m\left(np\right)^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

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

Cancel out mp in both numerator and denominator.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{1}{mn^{3}p^{3}}\right)^{1}$$

Calculate \frac{1}{mn^{3}p^{3}} to the power of 1 and get \frac{1}{mn^{3}p^{3}}.

$$\frac{1}{mn^{3}p^{3}}$$

Expand

$$\frac{1}{m\left(np\right)^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -2 and 3 to get 1.

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

Cancel out mp in both numerator and denominator.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{1}{mn^{3}p^{3}}\right)^{1}$$

Calculate \frac{1}{mn^{3}p^{3}} to the power of 1 and get \frac{1}{mn^{3}p^{3}}.

$$\frac{1}{mn^{3}p^{3}}$$