How do you multiply -\frac { 2} { 5} x ^ { 2} y ^ { 3} \cdot \frac { 5} { 7} x ^ { 4} y ^ { 4}?

May 15, 2017

$- \frac{2}{5} {x}^{2} {y}^{3} \cdot \frac{5}{7} {x}^{4} {y}^{4} = - \frac{7}{25} {x}^{6} {y}^{7}$

Written in decimal form: $- \frac{7}{25} {x}^{6} {y}^{7} = - 0.29 {x}^{6} {y}^{7}$

Explanation:

Given: $- \frac{2}{5} {x}^{2} {y}^{3} \cdot \frac{5}{7} {x}^{4} {y}^{4}$

Performing multiplication within an expression, we can move the fractions together:

$\left(- \frac{2}{5}\right) \left(\frac{5}{7}\right) {x}^{2} {y}^{3} \cdot {x}^{4} {y}^{4}$

Now we can add exponents (by the exponent rule of multipication):

$\left(- \frac{2}{\cancel{5}}\right) \left(\frac{\cancel{5}}{7}\right) {x}^{6} {y}^{7} = - \frac{2}{7} {x}^{6} {y}^{7} = - 0.29 {x}^{6} {y}^{7}$