Solve frac{2u^{3}v^4}{(2u^3*-2vu^2)^3}

$$\frac { 2 u ^ { 3 } v ^ { 4 } } { ( 2 u ^ { 3 } \cdot - 2 v u ^ { 2 } ) ^ { 3 } }$$

Evaluate

$$-\frac{v}{32u^{12}}$$

Solution Steps

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

$$\frac{2u^{3}v^{4}}{\left(2u^{5}\left(-2\right)v\right)^{3}}$$

Multiply 2 and -2 to get -4.

$$\frac{2u^{3}v^{4}}{\left(-4u^{5}v\right)^{3}}$$

Expand \left(-4u^{5}v\right)^{3}.

$$\frac{2u^{3}v^{4}}{\left(-4\right)^{3}\left(u^{5}\right)^{3}v^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{2u^{3}v^{4}}{\left(-4\right)^{3}u^{15}v^{3}}$$

Calculate -4 to the power of 3 and get -64.

$$\frac{2u^{3}v^{4}}{-64u^{15}v^{3}}$$

Cancel out 2u^{3}v^{3} in both numerator and denominator.

$$\frac{v}{-32u^{12}}$$

Expand

$$-\frac{v}{32u^{12}}$$

Solution Steps

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

$$\frac{2u^{3}v^{4}}{\left(2u^{5}\left(-2\right)v\right)^{3}}$$

Multiply 2 and -2 to get -4.

$$\frac{2u^{3}v^{4}}{\left(-4u^{5}v\right)^{3}}$$

Expand \left(-4u^{5}v\right)^{3}.

$$\frac{2u^{3}v^{4}}{\left(-4\right)^{3}\left(u^{5}\right)^{3}v^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{2u^{3}v^{4}}{\left(-4\right)^{3}u^{15}v^{3}}$$

Calculate -4 to the power of 3 and get -64.

$$\frac{2u^{3}v^{4}}{-64u^{15}v^{3}}$$

Cancel out 2u^{3}v^{3} in both numerator and denominator.

$$\frac{v}{-32u^{12}}$$