# 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.

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## 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 \( e \).
Answer

## 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 |

\( b^{x} \) | | | | | |

\( \dfrac{1}{b^x} \) | | | | | |

\( b^{-x} \) | | | | | |

## More References and Links

exponential

Rules of Logarithm and Exponential - Questions with Solutions

change of base formula

Maths Calculators and Solvers.