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

23 = 2 * 2 * 2 = 8

Many Scratchers have requested a block for calculating exponents, but such a block does not yet exist. Snap! and other Scratch modifications have a `(() ^ ()::operators)` block.

## 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 positive whole number powers.
```when flag clicked
ask [What is the base number?] and wait
ask [To what power?] and wait
set [ans v] to (1)
repeat ([abs v] of (2nd#))
set [ans v] to ((ans) * (1st#))
end
if <(2nd#) < > 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 mn and 10log mn = mn.

#### 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 00 so that it does not give an error then.
• The base is negative: If one wants to be able to do something such as xp 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 10x = -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) < > then
set [result v] to ((1) / (result))
end
``` Note: Positive rational exponents, e.g. 10½ 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.
```('%n ^ %n'						r	exp:of: - -)
```exp: b of: n