Solve frac{2mn^{3}}{n^-3*(2m^4n^3)^-4}

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

Evaluate

$$32m^{17}n^{18}$$

Solution Steps

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

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

Expand \left(2n^{3}m^{4}\right)^{-4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and -4 to get -12.

$$\frac{2mn^{6}}{2^{-4}n^{-12}\left(m^{4}\right)^{-4}}$$

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

$$\frac{2mn^{6}}{2^{-4}n^{-12}m^{-16}}$$

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

$$\frac{2mn^{6}}{\frac{1}{16}n^{-12}m^{-16}}$$

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

$$\frac{2m^{17}n^{18}}{\frac{1}{16}}$$

Divide 2m^{17}n^{18} by \frac{1}{16} by multiplying 2m^{17}n^{18} by the reciprocal of \frac{1}{16}.

$$2m^{17}n^{18}\times 16$$

Multiply 2 and 16 to get 32.

$$32m^{17}n^{18}$$

Expand

$$32m^{17}n^{18}$$

Solution Steps

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

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

Expand \left(2n^{3}m^{4}\right)^{-4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and -4 to get -12.

$$\frac{2mn^{6}}{2^{-4}n^{-12}\left(m^{4}\right)^{-4}}$$

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

$$\frac{2mn^{6}}{2^{-4}n^{-12}m^{-16}}$$

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

$$\frac{2mn^{6}}{\frac{1}{16}n^{-12}m^{-16}}$$

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

$$\frac{2m^{17}n^{18}}{\frac{1}{16}}$$

Divide 2m^{17}n^{18} by \frac{1}{16} by multiplying 2m^{17}n^{18} by the reciprocal of \frac{1}{16}.

$$2m^{17}n^{18}\times 16$$

Multiply 2 and 16 to get 32.

$$32m^{17}n^{18}$$