Introduction to powers and exponents. Learn the basics of exponential notation in Grade 9 Alberta mathematics curriculum.
Lesson 2.1 of Powers & Exponent Laws in Grade 9 Math — Alberta curriculum lessons.
When we multiply the same number over and over, we can write it as a power instead of repeating the multiplication.
For example:
3 is the base — the number being multiplied. 4 is the exponent — it tells us how many times the base is multiplied by itself.
Powers can be written in many different ways, but they all mean the same thing. You'll often see them written as repeated multiplication, exponential form, or expanded form.
Let's look at an example with the base number 3 and the exponent 4:
Example – The Power of 3.
All three mean the same thing — we're multiplying 3 by itself 4 times.
Important Question. What happens if we switch the base and exponent?
The base and exponent are not interchangeable. That means 2⁵ ≠ 5²
Let's check to see why:
Calculation.
They are not the same. The base and the exponent cannot be switched and still be equal.
Can you think of one example where switching the base and exponent gives the same answer — but you can't use the same number for both?
Hint. It's rare, but there is one!
Let's explore this:
Try 2⁴ and 4²:
Calculation.
Amazing Result!. Both give 16!
So the special pair is 2 and 4 — they can switch places and still give the same result.
This shows that while most powers change when you swap the base and exponent, this unique pair doesn't!
Let's take what we've learned about powers and look at two special types — square numbers and cube numbers.
A square number is what you get when you multiply a number by itself once.
In other words, a number is "squared" when it's raised to the power of 2.
For example:
Example. 4² = 4 × 4 = 16
We say "four squared equals sixteen."
The little 2 (the exponent) tells us we're making a square number.
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