Question

How do you simplify `(4a^2)(-3a)(-5a^4)` using the product of powers property?

Answer 1

The result is `60a^7`.

First of all, let's see that the sign is positive: one factor is positive, and two factors are negative, so the sign changes twice and it is + in the end.

Then, we simply multiply the coefficient: `4\cdot 3\cdot 5 = 60`

Finally, we multiply the powers of `a`: the product of powers property says that if we multiply two powers of the same base, we simply have to sum up the exponents, so `a^2\cdot a\cdot a^4 = a^{2+1+4}=a^7`.