Solve frac{(m^{-6}n^{5})^-3}{(4m^6n^-5)^2}

$$\frac { ( m ^ { - 6 } n ^ { 5 } ) ^ { - 3 } } { ( 4 m ^ { 6 } n ^ { - 5 } ) ^ { 2 } }$$

Evaluate

$$\frac{m^{6}}{16n^{5}}$$

Solution Steps

Expand \left(m^{-6}n^{5}\right)^{-3}.

$$\frac{\left(m^{-6}\right)^{-3}\left(n^{5}\right)^{-3}}{\left(4m^{6}n^{-5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and -3 to get 18.

$$\frac{m^{18}\left(n^{5}\right)^{-3}}{\left(4m^{6}n^{-5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{m^{18}n^{-15}}{\left(4m^{6}n^{-5}\right)^{2}}$$

Expand \left(4m^{6}n^{-5}\right)^{2}.

$$\frac{m^{18}n^{-15}}{4^{2}\left(m^{6}\right)^{2}\left(n^{-5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{m^{18}n^{-15}}{4^{2}m^{12}\left(n^{-5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -5 and 2 to get -10.

$$\frac{m^{18}n^{-15}}{4^{2}m^{12}n^{-10}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{m^{18}n^{-15}}{16m^{12}n^{-10}}$$

Cancel out m^{12} in both numerator and denominator.

$$\frac{n^{-15}m^{6}}{16n^{-10}}$$

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

$$\frac{m^{6}}{16n^{5}}$$

Expand

$$\frac{m^{6}}{16n^{5}}$$

Solution Steps

Expand \left(m^{-6}n^{5}\right)^{-3}.

$$\frac{\left(m^{-6}\right)^{-3}\left(n^{5}\right)^{-3}}{\left(4m^{6}n^{-5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -6 and -3 to get 18.

$$\frac{m^{18}\left(n^{5}\right)^{-3}}{\left(4m^{6}n^{-5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -3 to get -15.

$$\frac{m^{18}n^{-15}}{\left(4m^{6}n^{-5}\right)^{2}}$$

Expand \left(4m^{6}n^{-5}\right)^{2}.

$$\frac{m^{18}n^{-15}}{4^{2}\left(m^{6}\right)^{2}\left(n^{-5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{m^{18}n^{-15}}{4^{2}m^{12}\left(n^{-5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -5 and 2 to get -10.

$$\frac{m^{18}n^{-15}}{4^{2}m^{12}n^{-10}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{m^{18}n^{-15}}{16m^{12}n^{-10}}$$

Cancel out m^{12} in both numerator and denominator.

$$\frac{n^{-15}m^{6}}{16n^{-10}}$$

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

$$\frac{m^{6}}{16n^{5}}$$