# How do you simplify (-7x^4y^2)(-2x^2y^2)?

Mar 31, 2015

You can divide the calculation in three steps:

1. Firts of all, the sign: when multiplying two numbers, look at the sign of the factors. Same sign (which means $+ \cdot +$ or $- \cdot -$) gives a positive result, while the other cases (i.e. $+ \cdot -$ or $- \cdot +$) gives a negative result. Since you have the multiplication of two negative numbers, the result will be positive.
2. The numeric part: this is probably the easiest part: you simply need to multiply the two numbers. So, you have $7 \cdot 2 = 14$
3. Variables: When multiplying two variables, simply add the exponent: so ${x}^{4} \cdot {x}^{2} = {x}^{4 + 2} = {x}^{6}$, and ${y}^{2} \cdot {y}^{2} = {y}^{2 + 2} = {y}^{4}$.

After all, writing a power is just a short way for writing a product of several factors, all equal to each other. So, writing the expression in a more complicated fashion, you would have
$\left(- 7 {x}^{4} {y}^{2}\right) \left(- 2 {x}^{2} {y}^{2}\right) =$
$\left(- 7\right) \left(- 2\right) x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot x \cdot x \cdot y \cdot y$
Now, $\left(- 7\right) \left(- 2\right)$ is $14$ for what we said on points 1 and 2 above. Then, simply rearrange the variable and count them!
$\left(- 7\right) \left(- 2\right) x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot x \cdot x \cdot y \cdot y =$
$14 \cdot x \cdot x \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y = 14 {x}^{6} {y}^{4}$