# How do you simplify (2.68×10^-5)×(4.40×10^-8) ?

Jul 22, 2015

$\left(2.68 \times {10}^{- 5}\right) \times \left(4.40 \times {10}^{- 8}\right)$

$= \left(2.68 \times 4.40\right) \times \left({10}^{- 5} \times {10}^{- 8}\right)$

$= 11.792 \times {10}^{- 13}$

$= 1.1792 \times {10}^{- 12}$

#### Explanation:

Note that ${a}^{b} \cdot {a}^{c} = {a}^{b + c}$

So ${10}^{- 5} \times {10}^{- 8} = {10}^{- 5 + \left(- 8\right)} = {10}^{- 13}$

When we multiply the mantissas $2.68 \times 4.40$ the result is greater than $10$, so we divide it by $10$ and adjust the exponent accordingly to give the result in scientific notation.