Solve frac{(2m^{2}n)^{2}*3m^{4}n^5}{m^3n^2*4(mm)^2}

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

Evaluate

$$3mn^{5}$$

Solution Steps

Multiply m and m to get m^{2}.

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

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

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

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

$$\frac{\left(2m^{2}n\right)^{2}\times 3m^{4}n^{5}}{m^{7}n^{2}\times 4}$$

Cancel out n^{2}m^{4} in both numerator and denominator.

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

Expand \left(2nm^{2}\right)^{2}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 3 and 4 to get 12.

$$\frac{12n^{3}n^{2}m^{4}}{4m^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{12n^{5}m^{4}}{4m^{3}}$$

Cancel out 4m^{3} in both numerator and denominator.

$$3mn^{5}$$

Expand

$$3mn^{5}$$

Solution Steps

Multiply m and m to get m^{2}.

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

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

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

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

$$\frac{\left(2m^{2}n\right)^{2}\times 3m^{4}n^{5}}{m^{7}n^{2}\times 4}$$

Cancel out n^{2}m^{4} in both numerator and denominator.

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

Expand \left(2nm^{2}\right)^{2}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 3 and 4 to get 12.

$$\frac{12n^{3}n^{2}m^{4}}{4m^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{12n^{5}m^{4}}{4m^{3}}$$

Cancel out 4m^{3} in both numerator and denominator.

$$3mn^{5}$$