Solve frac{4m^{2}n^{2}}{(2m^{2})^{3}}div3(2mn^2)^2/18m^4n^3

$$\frac { 4 m ^ { 2 } n ^ { 2 } } { ( 2 m ^ { 2 } ) ^ { 3 } } \div \frac { 3 ( 2 m n ^ { 2 } ) ^ { 2 } } { 18 m ^ { 4 } n ^ { 3 } }$$

Evaluate

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

Solution Steps

Divide \frac{4m^{2}n^{2}}{\left(2m^{2}\right)^{3}} by \frac{3\times \left(2mn^{2}\right)^{2}}{18m^{4}n^{3}} by multiplying \frac{4m^{2}n^{2}}{\left(2m^{2}\right)^{3}} by the reciprocal of \frac{3\times \left(2mn^{2}\right)^{2}}{18m^{4}n^{3}}.

$$\frac{4m^{2}n^{2}\times 18m^{4}n^{3}}{\left(2m^{2}\right)^{3}\times 3\times \left(2mn^{2}\right)^{2}}$$

Cancel out 3 in both numerator and denominator.

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

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

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

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

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

Multiply 4 and 6 to get 24.

$$\frac{24m^{6}n^{5}}{\left(2m^{2}\right)^{3}\times \left(2mn^{2}\right)^{2}}$$

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

$$\frac{24m^{6}n^{5}}{2^{3}\left(m^{2}\right)^{3}\times \left(2mn^{2}\right)^{2}}$$

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

$$\frac{24m^{6}n^{5}}{2^{3}m^{6}\times \left(2mn^{2}\right)^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{24m^{6}n^{5}}{8m^{6}\times \left(2mn^{2}\right)^{2}}$$

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

$$\frac{24m^{6}n^{5}}{8m^{6}\times 2^{2}m^{2}\left(n^{2}\right)^{2}}$$

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

$$\frac{24m^{6}n^{5}}{8m^{6}\times 2^{2}m^{2}n^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{24m^{6}n^{5}}{8m^{6}\times 4m^{2}n^{4}}$$

Multiply 8 and 4 to get 32.

$$\frac{24m^{6}n^{5}}{32m^{6}m^{2}n^{4}}$$

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

$$\frac{24m^{6}n^{5}}{32m^{8}n^{4}}$$

Cancel out 8n^{4}m^{6} in both numerator and denominator.

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

Expand

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

Solution Steps

Divide \frac{4m^{2}n^{2}}{\left(2m^{2}\right)^{3}} by \frac{3\times \left(2mn^{2}\right)^{2}}{18m^{4}n^{3}} by multiplying \frac{4m^{2}n^{2}}{\left(2m^{2}\right)^{3}} by the reciprocal of \frac{3\times \left(2mn^{2}\right)^{2}}{18m^{4}n^{3}}.

$$\frac{4m^{2}n^{2}\times 18m^{4}n^{3}}{\left(2m^{2}\right)^{3}\times 3\times \left(2mn^{2}\right)^{2}}$$

Cancel out 3 in both numerator and denominator.

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

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

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

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

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

Multiply 4 and 6 to get 24.

$$\frac{24m^{6}n^{5}}{\left(2m^{2}\right)^{3}\times \left(2mn^{2}\right)^{2}}$$

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

$$\frac{24m^{6}n^{5}}{2^{3}\left(m^{2}\right)^{3}\times \left(2mn^{2}\right)^{2}}$$

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

$$\frac{24m^{6}n^{5}}{2^{3}m^{6}\times \left(2mn^{2}\right)^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{24m^{6}n^{5}}{8m^{6}\times \left(2mn^{2}\right)^{2}}$$

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

$$\frac{24m^{6}n^{5}}{8m^{6}\times 2^{2}m^{2}\left(n^{2}\right)^{2}}$$

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

$$\frac{24m^{6}n^{5}}{8m^{6}\times 2^{2}m^{2}n^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{24m^{6}n^{5}}{8m^{6}\times 4m^{2}n^{4}}$$

Multiply 8 and 4 to get 32.

$$\frac{24m^{6}n^{5}}{32m^{6}m^{2}n^{4}}$$

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

$$\frac{24m^{6}n^{5}}{32m^{8}n^{4}}$$

Cancel out 8n^{4}m^{6} in both numerator and denominator.

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