# How do you write (5.74*10^14)(3.53*10^9) in scientific notation?

Jun 12, 2018

$2.02622 \cdot {10}^{24}$

#### Explanation:

Multiply the numeric part:

$5.74 \cdot 3.53 = 20.2622$

Rewrite the numeric part in scientific notation: we only need one significant digit

$20.2622 = 2.02622 \cdot 10$

Multiply the exponential part using the rule ${a}^{b} \cdot {a}^{c} = {a}^{b + c}$:

${10}^{14} \cdot {10}^{9} = {10}^{14 + 9} = {10}^{23}$

Put everything together:

$2.02622 \cdot 10 \cdot {10}^{23} = 2.02622 \cdot {10}^{24}$