# How do you simplify 10^a * 10^b * 10^c?

May 13, 2016

${10}^{a} \cdot {10}^{b} \cdot {10}^{c} = {10}^{a + b + c}$

#### Explanation:

This is easiest to see if $a , b , c$ are positive integers:

${10}^{a} \cdot {10}^{b} \cdot {10}^{c}$

$= {\overbrace{10 \times 10 \times . . \times 10}}^{\text{a times" xx overbrace(10xx10xx..xx10)^"b times" xx overbrace(10xx10xx..xx10)^"c times}}$

$= {\overbrace{10 \times 10 \times . . \times 10}}^{\text{a + b + c times}}$

$= {10}^{a + b + c}$

In fact, this works for any Real values of $a$, $b$ and $c$.