Laws of Exponents for Multiplication & Division

The exponent of a number tells you how many times to multiply the number. The rules of exponents follow the logic of how numerical values interact with each other. Some students choose simply to memorize the rules and apply them in class. Taking advantage of the opportunity to do extra worksheets and problems, without the pressure of turning them in, increases a student's ability to understand the logic, which makes it easier to remember the rules.

Exponents

The law of exponents simply means to multiply the number that many times by itself. For example:

8³ = 8 x 8 x 8 = 512
8 x 8 = 64 then 64 x 8 = 512.

Negative Numbers

The opposite of multiplication is division. When an exponent is a negative number, divide instead of multiply. For example:

3 ֿ² = 1/3² = 1/9

This is only true when the exponent is not 0.

Zero

Any number to the 0 power equals 1. For example:

1º = 1
2º = 1
12º = 1
0º = 1

Fractional Exponents

Sometimes the exponent itself is a fraction, and fractional exponents are also called radicals. For example:

x¹/ⁿ

The answer = x to the nth root. For example:

27¹/³ = (27¹/³)³ = ³√27 = 9.

Remember this: x¹/ⁿ = (x¹/ⁿ)ⁿ = n root of x.
100¹/² = (100¹/²)² = square root of 100 = 10

Distribution

Take the equation:

(xⁿⁿ)ⁿ this is the same as: xⁿⁿ ⁿ. For example:

(3³)² = 3³*² = 3 to the 6th power = 3x3x3x3x3x3 = 729

References

• Math is Fun: Exponents
• Laws of Exponents
• Purple Math: Basic Rule of Exponents

Resources

• Read this Article in Spanish
• Exponent Worksheets