Solve frac{(8m^{7}n^{5})^{2}}{(2^2m^3n^2)^3}

$$\frac { ( 8 m ^ { 7 } n ^ { 5 } ) ^ { 2 } } { ( 2 ^ { 2 } m ^ { 3 } n ^ { 2 } ) ^ { 3 } }$$

Evaluate

$$n^{4}m^{5}$$

Solution Steps

Expand \left(8m^{7}n^{5}\right)^{2}.

$$\frac{8^{2}\left(m^{7}\right)^{2}\left(n^{5}\right)^{2}}{\left(2^{2}m^{3}n^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{8^{2}m^{14}\left(n^{5}\right)^{2}}{\left(2^{2}m^{3}n^{2}\right)^{3}}$$

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

$$\frac{8^{2}m^{14}n^{10}}{\left(2^{2}m^{3}n^{2}\right)^{3}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{64m^{14}n^{10}}{\left(2^{2}m^{3}n^{2}\right)^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{64m^{14}n^{10}}{\left(4m^{3}n^{2}\right)^{3}}$$

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

$$\frac{64m^{14}n^{10}}{4^{3}\left(m^{3}\right)^{3}\left(n^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{64m^{14}n^{10}}{4^{3}m^{9}\left(n^{2}\right)^{3}}$$

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

$$\frac{64m^{14}n^{10}}{4^{3}m^{9}n^{6}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64m^{14}n^{10}}{64m^{9}n^{6}}$$

Cancel out 64n^{6}m^{9} in both numerator and denominator.

$$n^{4}m^{5}$$

Expand

$$n^{4}m^{5}$$

Solution Steps

Expand \left(8m^{7}n^{5}\right)^{2}.

$$\frac{8^{2}\left(m^{7}\right)^{2}\left(n^{5}\right)^{2}}{\left(2^{2}m^{3}n^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{8^{2}m^{14}\left(n^{5}\right)^{2}}{\left(2^{2}m^{3}n^{2}\right)^{3}}$$

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

$$\frac{8^{2}m^{14}n^{10}}{\left(2^{2}m^{3}n^{2}\right)^{3}}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{64m^{14}n^{10}}{\left(2^{2}m^{3}n^{2}\right)^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{64m^{14}n^{10}}{\left(4m^{3}n^{2}\right)^{3}}$$

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

$$\frac{64m^{14}n^{10}}{4^{3}\left(m^{3}\right)^{3}\left(n^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{64m^{14}n^{10}}{4^{3}m^{9}\left(n^{2}\right)^{3}}$$

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

$$\frac{64m^{14}n^{10}}{4^{3}m^{9}n^{6}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64m^{14}n^{10}}{64m^{9}n^{6}}$$

Cancel out 64n^{6}m^{9} in both numerator and denominator.

$$n^{4}m^{5}$$