Question

Simplify the expression (3a4)(−6a3) . Show your work and justify each step.

Answer 1

I'm going to assume the 4 and 3 are exponents and the expression is $\left(3a^4\right)\left(-6a^3\right)$.

The first step is to separate the coefficients of 3 and -6 from the variables and to multiply those as normal:

    $3 \cdot (-6) = -18$

As for the variables, you want to recognize that $a^4$ means $a \cdot a \cdot a \cdot a$ and $a^3$ means $a \cdot a \cdot a$, so

    $a^4 \cdot a^3 = \left( a \cdot a \cdot a \cdot a\right) \cdot \left(a \cdot a \cdot a\right)$

In total, there are 7 a's being multiplied, so

    $a^4 \cdot a^3 = a^{4+3} = a^7$

Putting this all together, we have:

    $\left(3a^4\right)\left(-6a^3\right) = 18a^7$