Solve frac{m^{3}n^3*(25m^2n^2)^2}{m}

$$\frac { m ^ { 3 } n ^ { 3 } \times ( 25 m ^ { 2 } n ^ { 2 } ) ^ { 2 } } { m }$$

Evaluate

$$625m^{6}n^{7}$$

Solution Steps

Cancel out m in both numerator and denominator.

$$m^{2}n^{3}\times \left(25m^{2}n^{2}\right)^{2}$$

Expand \left(25m^{2}n^{2}\right)^{2}.

$$m^{2}n^{3}\times 25^{2}\left(m^{2}\right)^{2}\left(n^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$m^{2}n^{3}\times 25^{2}m^{4}\left(n^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$m^{2}n^{3}\times 25^{2}m^{4}n^{4}$$

Calculate 25 to the power of 2 and get 625.

$$m^{2}n^{3}\times 625m^{4}n^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$m^{6}n^{3}\times 625n^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$m^{6}n^{7}\times 625$$

Expand

$$625m^{6}n^{7}$$

Solution Steps

Cancel out m in both numerator and denominator.

$$m^{2}n^{3}\times \left(25m^{2}n^{2}\right)^{2}$$

Expand \left(25m^{2}n^{2}\right)^{2}.

$$m^{2}n^{3}\times 25^{2}\left(m^{2}\right)^{2}\left(n^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$m^{2}n^{3}\times 25^{2}m^{4}\left(n^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$m^{2}n^{3}\times 25^{2}m^{4}n^{4}$$

Calculate 25 to the power of 2 and get 625.

$$m^{2}n^{3}\times 625m^{4}n^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$m^{6}n^{3}\times 625n^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$m^{6}n^{7}\times 625$$