Key takeaway: An exponent is a small raised number telling how many times a base is used as a factor, so 7 with an exponent of 4 means 7 × 7 × 7 × 7 = 2,401.
Grade 66.EE.A.1Numbers and Operations
Definition of Exponent
An exponent shortens a long chain of identical factors. You write the repeated number once, the base, and put a small count above and to its right.
The whole expression is called a power and is read “7 to the fourth power”. Squared and cubed are special names for exponents 2 and 3, because they give the area of a square and the volume of a cube. A nonzero base raised to 0 equals 1, and a power of 1 leaves the base unchanged.
Formula and notation
The base is the number being multiplied, and the small number counts the factors:
\[b^{n} = b \times b \times \text{…} \times b \quad (n \text{ factors})\]
Parentheses show what is being raised: \((-2)^4 = 16\), but \(-2^4 = -16\), because only the 2 is raised to the power in the second case.
Key facts
- The count of factors is the exponent; it is not a number to multiply the base by.
- A negative base gives a positive result when the count is even, negative when odd.
- Squares come from area and cubes from volume, which explains where those names come from.
- Powers are evaluated before multiplication, division, addition and subtraction.
Exponent example
Write \(7 \times 7 \times 7 \times 7\) with an exponent and find its value. Then evaluate \(6^3 – 3^4\).
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Four factors of 7 give \(7^4\).
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Multiply in stages: \(7 \times 7 = 49\), \(49 \times 7 = 343\), \(343 \times 7 = 2{,}401\).
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For the second expression, \(6^3 = 216\) and \(3^4 = 81\), so \(216 – 81 = 135\).
\(7^4 = \) 2,401 and \(6^3 – 3^4 = \) 135.
Common mistake
Watch out
Pablo computes \(7^4\) as \(7 \times 4 = 28\).
Why it is wrong
The small number counts the factors; it is not a multiplier. \(7^4\) is a product of four sevens, far bigger than 28. A quick check: \(7^2 = 49\) already beats 28.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Numbers and Operations