Exponents
Understand and apply exponent laws
What are Exponents?
An exponent tells you how many times to multiply a base number by itself. We write it as a small number above and to the right of the base. For example, 2^3 means 2 × 2 × 2 = 8. The base is 2 and the exponent is 3.
Example
Calculating Powers
3^2 = 3 × 3 = 9 (read: '3 squared' or '3 to the power of 2')
5^3 = 5 × 5 × 5 = 125 (read: '5 cubed' or '5 to the power of 3')
2^4 = 2 × 2 × 2 × 2 = 16
10^3 = 10 × 10 × 10 = 1 000
Laws of Exponents
When multiplying same bases: a^m × a^n = a^(m+n). Example: 2^3 × 2^4 = 2^7 = 128.
When dividing same bases: a^m ÷ a^n = a^(m-n). Example: 5^6 ÷ 5^2 = 5^4 = 625.
Power of zero: a^0 = 1 (any number to the power 0 is 1).
Example
Worked Examples
Simplify: 3^2 × 3^3 = 3^(2+3) = 3^5 = 243
Simplify: 4^5 ÷ 4^3 = 4^(5-3) = 4^2 = 16
Evaluate: 7^0 = 1
Simplify: (2^3)^2 = 2^(3×2) = 2^6 = 64
Note
Remember
Exponent = how many times to multiply the base by itself. Multiplying same bases → add exponents. Dividing same bases → subtract exponents. Anything to the power of 0 equals 1.
Key Vocabulary
ExponentThe small number that shows how many times to multiply
BaseThe number being multiplied by itself
PowerAnother word for exponent, e.g. 'to the power of 3'
SquaredRaised to the power of 2
CubedRaised to the power of 3
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Exponent
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