Solve frac{(3m^{2}n)^{3}*(2mn^2)^2}{7m^2n^3}

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

Evaluate

$$\frac{108n^{4}m^{6}}{7}$$

Solution Steps

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

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

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

$$\frac{3^{3}m^{6}n^{3}\times \left(2mn^{2}\right)^{2}}{7m^{2}n^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27m^{6}n^{3}\times \left(2mn^{2}\right)^{2}}{7m^{2}n^{3}}$$

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

$$\frac{27m^{6}n^{3}\times 2^{2}m^{2}\left(n^{2}\right)^{2}}{7m^{2}n^{3}}$$

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

$$\frac{27m^{6}n^{3}\times 2^{2}m^{2}n^{4}}{7m^{2}n^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{27m^{6}n^{3}\times 4m^{2}n^{4}}{7m^{2}n^{3}}$$

Multiply 27 and 4 to get 108.

$$\frac{108m^{6}n^{3}m^{2}n^{4}}{7m^{2}n^{3}}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{108m^{8}n^{3}n^{4}}{7m^{2}n^{3}}$$

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

$$\frac{108m^{8}n^{7}}{7m^{2}n^{3}}$$

Cancel out m^{2}n^{3} in both numerator and denominator.

$$\frac{108n^{4}m^{6}}{7}$$

Expand

$$\frac{108n^{4}m^{6}}{7}$$

Solution Steps

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

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

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

$$\frac{3^{3}m^{6}n^{3}\times \left(2mn^{2}\right)^{2}}{7m^{2}n^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27m^{6}n^{3}\times \left(2mn^{2}\right)^{2}}{7m^{2}n^{3}}$$

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

$$\frac{27m^{6}n^{3}\times 2^{2}m^{2}\left(n^{2}\right)^{2}}{7m^{2}n^{3}}$$

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

$$\frac{27m^{6}n^{3}\times 2^{2}m^{2}n^{4}}{7m^{2}n^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{27m^{6}n^{3}\times 4m^{2}n^{4}}{7m^{2}n^{3}}$$

Multiply 27 and 4 to get 108.

$$\frac{108m^{6}n^{3}m^{2}n^{4}}{7m^{2}n^{3}}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{108m^{8}n^{3}n^{4}}{7m^{2}n^{3}}$$

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

$$\frac{108m^{8}n^{7}}{7m^{2}n^{3}}$$

Cancel out m^{2}n^{3} in both numerator and denominator.

$$\frac{108n^{4}m^{6}}{7}$$