# How do you multiply (2 x 10^4)(4.1 x 10^3)?

Apr 11, 2015

Remember the associative rule that allows us to rearrange the order of terms in a multiplication: $a \times b \times c \times d = a \times c \times b \times d$

and the product rule for exponents:
${b}^{p} \times {b}^{q} = {b}^{p + q}$

So
$\left(2 \times {10}^{4}\right) \left(4.1 \times {10}^{3}\right)$

$= \left(2 \times 4.1\right) \times \left({10}^{4} \times {10}^{3}\right)$

$= 8 , 2 \times {10}^{7}$