Multiply Same Bases
Keep the base. Add the exponents.
x³ × x⁴Keep xAdd: 3 + 4 = 7Answer: x⁷Rules & properties reference
Exponent Rules
An exponent is the small raised number. It tells how many times to multiply the base by itself.
In simple words:In 3⁴, the 3 is the base and the raised 4 is the exponent. It means 3 × 3 × 3 × 3.
Exponent form3⁴
Multiply it out3 × 3 × 3 × 3 = 81
See the parts
Base and Exponent
34
↑BaseThe number being multiplied
↑ExponentHow many 3s to multiply
Why should I care?
Exponents are a shorter way to show repeated multiplication. They are used for area, volume, very large numbers, science, money growth, and computer storage.
Quick-reference chart
The Rules
Read the rule, then study the example.
Divide Same Bases
Keep the base. Subtract the exponents.
a⁸ ÷ a³Keep aSubtract: 8 - 3 = 5Answer: a⁵Power Raised to a Power
Keep the base. Multiply the exponents.
(m²)⁵Keep mMultiply: 2 · 5 = 10Answer: m¹⁰Power Outside Parentheses
Give the outside exponent to every part inside.
(2x)³2³ × x³8 × x³Answer: 8x³Zero Exponent
A nonzero number with an exponent of 0 equals 1.
7⁰Answer: 1Negative Exponent
Move the power across the fraction bar. The exponent becomes positive.
Example 1: Variablex⁻³Move x³ below 11x³Example 2: Number2⁻³1 ÷ 2³ = 1 ÷ 818A negative exponent does not make the answer negative.Follow the thinking
Worked Examples
Simplify x⁵ × x²
- The base is x in both powers.
- Keep the x.
- Add the exponents: 5 + 2 = 7.
x⁵ × x² = x⁷
Simplify (3y²)³
- Give the outside 3 to both parts.
- For 3³: 3 · 3 · 3 = 27.
- For (y²)³: multiply 2 · 3 = 6.
(3y²)³ = 27y⁶
Watch out
Common Mistakes
- Do not multiply exponents when multiplying the same base. Add them.
- A zero exponent does not make the answer zero. A nonzero base with exponent 0 equals 1.
- An outside exponent must go to every part inside the parentheses.
Check yourself
Quick Practice
1. b⁴ × b⁶
b¹⁰. Keep b and add 4 + 6.
2. z⁹ ÷ z⁴
z⁵. Keep z and subtract 9 - 4.
3. (x³)⁴
x¹². Keep x and multiply 3 · 4.
Your turn
10-Question Exponent Practice
Type the base followed by its exponent. For example, you may type x7 for x⁷.
Finished with this resource?