Exponents are a short way to show repeated multiplication. Instead of writing the same number multiplied many times, we use an exponent to make it simpler and faster to read.
Parts of an Exponent
a^n
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Base (a) → the number being multiplied
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Exponent (n) → tells how many times the base is used as a factor
Example
3^4 = 3×3×3×3=81
Why Are Exponents Useful?
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They make large numbers easier to write
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They are used in science, technology, money, and geometry
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They help describe patterns and growth
Common Exponents You Should Know
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a^1 = a (any number to the power of 1 is itself)
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a^0 = 1 (any number except 0 raised to 0 equals 1)
Example:
5^0 = 1
Laws (Rules) of Exponents
1. Product of Powers Rule
When multiplying powers with the same base, add the exponents.
a^m × a^n = a^(m+n)
Example:
2^3 × 2^4 = 2^7
2. Quotient of Powers Rule
When dividing powers with the same base, subtract the exponents.
a^m ÷ a^n = a^(m−n)
Example:
5^6 ÷ 5^2 = 5^4
3. Power of a Power Rule
Multiply the exponents.
(a^m)^n = a^(m×n)
Example:
(3^2)^3 = 3^6
4. Power of a Product
Distribute the exponent to each factor.
(ab)^n = a^(n) * b^(n)
Example:
(2×3)^2 = 2^2 × 3^2
Negative Exponents
A negative exponent means take the reciprocal.
a^(−n) = 1/a^n
Example:
2^(−3) = 1/(2^3)=1/8