# How do you multiply (7xx10^-6)(6xx10^-3)?

May 12, 2018

$= 4.2 \times {10}^{-} 8$

#### Explanation:

Compare this question with an algebraic product:

$3 {x}^{5} \times 5 {x}^{2}$

We would not hesitate in multiplying the numbers and then adding the indices of the same bases, $x$.

$3 {x}^{5} \times 5 {x}^{2} = 3 \times 5 \times {x}^{5} \times {x}^{2}$

$= 15 {x}^{7}$

Do exactly the same with the numbers in scientific notation.

Multiply the numbers and then adding the indices of the same bases, $10$.

$7 \times {10}^{-} 6 \times {10}^{-} 3$

$= 7 \times 6 \times {10}^{-} 6 \times {10}^{-} 3$

$= 42 \times {10}^{-} 9$

Change to scientific notation. $42 = 4.2 \times 10$

$= 4.2 \times {10}^{-} 8$