# Exponential Function Calculator

An easy to use calculator to compute exponential functions of the form $b^x$ to any base $b$ is presented. Activities related to the product and quotient of like bases exponential rules described below, using the calculator, are also included.



## Basic Rules of Exponential Functions

The exponential function $b^x$ is defined for $b \gt 0$ and $b \ne 1$
1 - Product of Like Bases Rule
$b^x b^y = b^{x+y}$
2 - Quotient of Like Bases Rule
$\dfrac{b^x}{b^y} = b^{x-y}$

## Use Exponential Calculator

Enter the argument $x$ of the logarithmic function and its base $b$ such that
$x \gt 0$ , $b \gt 0$ and $b \ne 1$
The output of the calculator is the exponential function $b^x$.
NOTE that natural base $e$ is entered as the letter $e$.

 Argument: $\quad x =$ 3 Base: $\quad b =$ 3 Decimal Places Desired = 5

## Activities Using the Exponential Calculator

Activity 1: Product and Quotient of Like Bases Rules
Chose any base $b$ and use the calculator to find the values of   $b^x$, $b^y$, $b^{x+y}$, $b^x \cdot b^y$, $\dfrac{b^x}{b^y}$ and $b^{x-y}$
a) Compare the quantites   $b^x \cdot b^y$ and   $b^{x+y}$ for each pair of values $(x,y)$. These quantities are equal according to the product rule of like bases in 1) above.
b) Compare the quantites   $\dfrac{b^x}{b^y}$ and   $b^{x-y}$ for each pair of values $(x,y)$. These quantities are equal according to the quotient of like bases rule in 2) above.

 $x$ 4 5 25 40 100 120 1000 $b^x$ $y$ 2 4 5 10 25 60 100 $b^y$ $\color{red}{b^x \cdot b^y}$ $\color{red}{b^{x+y}}$ $\color{blue}{\dfrac{b^x}{b^y}}$ $\color{blue}{b^{x-y}}$

Activity 2: Negative Exponents
The negative exponent is defined as follows $b^{-x} = \dfrac{1}{b^x}$
Use the calculator to calculate $b^x$ and $b^{-x}$ and compare the quantities $b^{-x}$ and $\dfrac{1}{b^x}$ which according to the definition above are equal.

 $x$ 4 5 25 40 100 $b$ e 3 4 5 10 $b^{x}$ $\dfrac{1}{b^x}$ $b^{-x}$