Question

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

Answer 1

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 `+ * +` or `- * -`) gives a positive result, while the other cases (i.e. `+ * -` or `- * +`) 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*2=14`
3. Variables: When multiplying two variables, simply add the exponent: so `x^4*x^2 = x^{4+2} = x^6`, and `y^2 * 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
`(-7x^4y^2)(-2x^2y^2) =`
`(-7)(-2)x*x*x*x*y*y*x*x*y*y`
Now, `(-7)(-2)` is `14` for what we said on points 1 and 2 above. Then, simply rearrange the variable and count them!
`(-7)(-2)x*x*x*x*y*y*x*x*y*y=`
`14*x*x*x*x*x*x*y*y*y*y=14x^6y^4`