Question

Very small numbers are often written in exponential form using scientific notation to make them easier to multiply or divide. Explain how to apply the laws of exponents when multiplying and dividing numbers written in scientific notation.
Please give a detailed and accurate explanation that demonstrates a full understanding. Thanks for any help. :)

Answer 1

The laws of exponents that are applied in standard form are:

$x^m*x^n=x^{m+n}$
$\frac{x^m}{x^n} =x^{m-n}$

Example 1:
(6.25 × 10⁴) × (2.53 × 10⁻⁹)
(6.25×2.53) × (10⁴×10⁻⁹)
15.8125 × 10⁽⁴ ⁺ ⁻⁹⁾
15.8125×10⁻⁵

Example 2:
(3.65×10⁵) ÷ (1.45×10⁻²) 
(3.65÷1.45) × (10⁵÷10⁻²)
2.52×10⁽⁵ ⁻ ⁽⁻²⁾⁾
2.52×10⁵⁺²
2.52×10⁷