## Calculus 8th Edition

$b^{x-y}=\frac{b^{x}}{b^{y}}$ This is known as second Law of Exponents; where x and y are real numbers.
We already know that $b^{x}=e^{xlnb}$ Now, $b^{x-y}=e^{(x-y)lnb}$ This implies $b^{x-y}=e^{xlnb-ylnb}=\frac{e^{xlnb}}{e^{ylnb}}$ Hence, $b^{x-y}=\frac{b^{x}}{b^{y}}$ This is known as second Law of Exponents; where x and y are real numbers.