Exponent
In short: Exponent is the raised mini-number that counts how many copies of the base get multiplied together, which makes 3 to the 4th power equal 81.
6th GradeNumbers and Operations6.EE.A.1
What is Exponent?
Every exponent is shorthand for repeated multiplication. Rather than writing \(5 \times 5 \times 5 \times 5 \times 5 \times 5\), you write \(5^6\) and read it “five to the sixth power”.
Precisely, in \(b^n\) the number \(b\) is the base and the whole number \(n\) counts the equal factors, so \(b^n = b \cdot b \cdots b\) with \(n\) copies of \(b\). The special cases are \(b^1 = b\), and powers of 10 such as \(10^3 = 1{,}000\).
How to spot it
- A small raised number sits at the upper right of a base, as in \(7^2\) or \(2^{10}\).
- A quantity doubles, triples or halves again and again, like bacteria in a dish.
- Squares and cubes appear in area and volume formulas, such as \(s^2\) and \(s^3\).
- A very large number is written compactly using powers of 10.
The method
- Identify the base, the big number, and the exponent, the small raised one.
- Write the base out as many times as the exponent says: \(4^5 = 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4\).
- Multiply in pairs to keep the work tidy: \(16 \cdot 16 \cdot 4\) after combining the first four.
- State the result and check that you did not multiply the base by the exponent.
Exponent: solved example
Problem
A video posted by a school in Raleigh is shared so that every viewer sends it to 4 new viewers, round after round. How many new viewers watch it in round 5 if only the first sender starts?
Solution
Round 1 reaches 4 viewers, and each round multiplies by 4, so round 5 reaches \(4^5\).
Compute: \(4 \cdot 4 = 16\), \(16 \cdot 4 = 64\), \(64 \cdot 4 = 256\), \(256 \cdot 4 = 1{,}024\). Round 5 reaches 1,024 viewers.
Try it
Question 1
Evaluate \(2^7\).
Show the answer
\(2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 128\).
Question 2
Explain why \(6^3\) is not 18.
Show the answer
\(6^3\) means \(6 \cdot 6 \cdot 6 = 216\); 18 comes from \(6 \cdot 3\), which confuses the exponent with a multiplier.
Exponent vs. Coefficient
In \(5x^3\), the 5 in front is the coefficient and it multiplies once, while the small 3 up high counts how many times \(x\) is a factor. Changing the 5 scales the result; changing the 3 changes the whole growth pattern.
Keep going
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Related words
Whole dictionary: A–Z · 6th Grade · Numbers and Operations