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=== Repeat Method === | === Repeat Method === | ||

{{note|This method can only be used with whole number powers}} | {{note|This method can only be used with whole number powers}} | ||

− | This script will be able to solve exponents | + | This script will be able to solve exponents of any base. however, it cannot handle fractional powers. |

<scratchblocks> | <scratchblocks> |

## Revision as of 15:38, 12 January 2020

**Solving exponents** is the process of multiplying a number (the *base*) by itself a number (the *power*) of times. For example:

**2 ^{3} = 2 * 2 * 2 = 8**

Many Scratchers have requested a block for calcuating exponents,^{[1]} but such a block does not yet exist.

## Contents

## Methods for calculating exponents in Scratch

There are multiple workarounds for solving exponents in Scratch.

### Repeat Method

Note: | This method can only be used with whole number powers |

This script will be able to solve exponents of any base. however, it cannot handle fractional powers.

when flag clicked ask [What is the base number?] and wait set [1st# v] to (answer) ask [To what power?] and wait set [2nd# v] to (answer) set [ans v] to (1) repeat ([abs v] of (2nd#)) set [ans v] to ((ans) * (1st#)) end if <(2nd#) < [0]> then set [ans v] to ((1) / (ans)) // a quick workaround for negative powers end say (join [The answer is: ] (ans)) for (2) secs

#### How it Works

- The Variable "1st#" is the base number. This is the number that will be multiplied by.
- The Variable "2nd#" determines how many times to repeat the multiplication.
- The variable "ans" is the answer, which is the number 1 multiplied by "1st#", "2nd#" times.

### Logarithmic Method

The logarithm method is much faster than the repeat method, but can not be used with negative bases.

(round ([10 ^ v] of ((power) * ([log v] of ([abs v] of (base))))))

or

(round ([e ^ v] of ((power) * ([ln v] of ([abs v] of (base))))))

#### How it Works

- The variable "base" is the base and the variable "power" is the power, or the number of times the base is multiplied. The reported value is the answer.
- The math works because n * log m = log m
^{n}and 10^{log mn}= m^{n}.

#### Special Cases

These are some cases that the above method will fail to calculate correctly:

- The base is 0: Since log 0 is undefined, have an if-else that gives
*0*for the answer if the base is 0, as long as the power is positive. The answer*1*should be given for 0^{0}so that it does not give an error then.

- The base is negative: If one wants to be able to do something such as x
^{p}where p is an integer, and they want to allow x to be negative, then the solution with logarithms will not work, because log(-1) is undefined (there is no solution to 10^{x}= -1). Ways to solve this are:- Use the loop multiplication method, and even just use loop multiplication / division whenever the power is an integer.
- Factor out the negative and find the answer for the absolute value of the exponent, then divide 1 by it if the exponent is negative. Also, it's a good idea to use an if block for whether p is odd or even ( if p mod 2 = 0 then p is even).

set [result v] to ([abs v] of (base)) // used to spread out math over two lines set [result v] to ([e^ v] of ((power)*([ln v] of (result)))::operators) if<(base) < [0]> then set [result v] to ((1) / (result)) end

Note: | Positive rational exponents, e.g. 10^{½} do work. Thus, this can be used to find N-roots of numbers. |

## Editing Scratch

This article or section documents something not included in the current version of Scratch (3.0). It is only useful from a historical perspective. |

*See also: Blockmaking FAQs*

Scratch can be modified to add a block which solves exponents. This is simplest to do in Scratch 1.4 and previous versions. The block specification is:

```
('%n ^ %n' r exp:of: - -)
```

and the method is:

```
exp: b of: n
^ b raisedTo: n
```