L5 · Powers: base and exponent

Learning goal

“I can write repeated multiplication as a power, expand a power back into a multiplication, and find its value — and I can use powers to write prime factorizations the short way.”

Power — a shorthand for repeated multiplication, like 3² (read “3 squared” or “3 to the power of 2”).

Base — the number being multiplied repeatedly. In 3², the base is 3.

Exponent — the small raised number that counts how many copies of the base are multiplied. In 3², the exponent is 2.

Worked example

Write 3 × 3 as a power. The base is 3 (the number being multiplied). Count the copies: 2 copies. So 3 × 3 = 3² = 9. The array shows why it's called “squared”: 3 rows of 3 tiles. Now a cube: 2 × 2 × 2 has 3 copies of the base 2, so it is 2³ = 8 — the model is a 2-by-2-by-2 block of 8 unit cubes. Say the rule plainly: exponent = number of copies of the base in the multiplication.

Check yourself — explain it

In 5³, what does the 3 tell you?

Paired problem — example still visible

Write 6 × 6 × 6 as a power and find its value. → 6³ = 216

Faded completion — last step is yours

“10 × 10 = 10^___, and its value is ___.” → Exponent 2; value 100

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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