Solve frac{2u^{4}v^{3}*-u^{2}v^4}{(-2u^0v^3)^4}

$$\frac { 2 u ^ { 4 } v ^ { 3 } \cdot - u ^ { 2 } v ^ { 4 } } { ( - 2 u ^ { 0 } v ^ { 3 } ) ^ { 4 } }$$

Evaluate

$$-\frac{u^{6}}{8v^{5}}$$

Short Solution Steps

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

$$\frac{2u^{4}v^{7}\left(-u^{2}\right)}{\left(-2u^{0}v^{3}\right)^{4}}$$

Calculate u to the power of 0 and get 1.

$$\frac{2u^{4}v^{7}\left(-u^{2}\right)}{\left(-2v^{3}\right)^{4}}$$

Expand \left(-2v^{3}\right)^{4}.

$$\frac{2u^{4}v^{7}\left(-u^{2}\right)}{\left(-2\right)^{4}\left(v^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{2u^{4}v^{7}\left(-u^{2}\right)}{\left(-2\right)^{4}v^{12}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{2u^{4}v^{7}\left(-u^{2}\right)}{16v^{12}}$$

Cancel out 2v^{7} in both numerator and denominator.

$$\frac{\left(-u^{2}\right)u^{4}}{8v^{5}}$$

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

$$\frac{-u^{6}}{8v^{5}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{u^{6}}{-8v^{5}}$$

Expand

$$-\frac{u^{6}}{8v^{5}}$$

Short Solution Steps

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

$$\frac{2u^{4}v^{7}\left(-u^{2}\right)}{\left(-2u^{0}v^{3}\right)^{4}}$$

Calculate u to the power of 0 and get 1.

$$\frac{2u^{4}v^{7}\left(-u^{2}\right)}{\left(-2v^{3}\right)^{4}}$$

Expand \left(-2v^{3}\right)^{4}.

$$\frac{2u^{4}v^{7}\left(-u^{2}\right)}{\left(-2\right)^{4}\left(v^{3}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{2u^{4}v^{7}\left(-u^{2}\right)}{\left(-2\right)^{4}v^{12}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{2u^{4}v^{7}\left(-u^{2}\right)}{16v^{12}}$$

Cancel out 2v^{7} in both numerator and denominator.

$$\frac{\left(-u^{2}\right)u^{4}}{8v^{5}}$$

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

$$\frac{-u^{6}}{8v^{5}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{u^{6}}{-8v^{5}}$$