Repeated factors → exponent
Count how many times the base appears; that count is the exponent. 2x means x doubled; x² means x times itself.
Why it works
x·x·x·x = x⁴.
Powers · What is a power? · 1.2
x² is x·x, not 2x.
A variable power means repeated multiplication, not multiplication by the exponent. x² = x·x (NOT 2x); x³ = x·x·x. Writing repeated factors as a power is the whole idea.
See it work.
Watch the method
x² is x·x, not 2x
x·x·x is x multiplied 3 times = x³.
1
Count the equal factors
Each repeated base becomes an exponent — the count of how many times it appears.
2
Write as a power
The coefficient stays in front; the repeated variable becomes a power.
The idea underneath.
From easy to tricky.
Write as a single power: z · z · z · z
1
Count the equal factors
Each repeated base becomes an exponent — the count of how many times it appears. z · z · z · z
2
Write as a power
The coefficient stays in front; the repeated variable becomes a power. = z^4
Write as a single power: y · y · y · y
1
Count the equal factors
Each repeated base becomes an exponent — the count of how many times it appears. y · y · y · y
2
Write as a power
The coefficient stays in front; the repeated variable becomes a power. = y^4
Write as a single power: x · x
1
Count the equal factors
Each repeated base becomes an exponent — the count of how many times it appears. x · x
2
Write as a power
The coefficient stays in front; the repeated variable becomes a power. = x^2
Where students slip.
Trap
Reading x² as 2x.
Fix
x² = x·x; 2x = x + x. They are different.
Trap
Reading x³ as 3x.
Fix
x³ = x·x·x.
Test yourself.
The Test
12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.
0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so
t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).Core
Core (4)
C1
Write as a single power: 3 · y · y
Need a hint?
- Count how many x’s are multiplied.
- That count is the exponent.
C2
Write as a single power: y · y
Need a hint?
- Count how many x’s are multiplied.
- That count is the exponent.
C3
Write as a single power: 2 · y · y
Need a hint?
- Count how many x’s are multiplied.
- That count is the exponent.
C4
Write as a single power: 2 · y · y · y · y
Need a hint?
- Count how many x’s are multiplied.
- That count is the exponent.
Apply
Apply (4)
A1
Write as a single power: y · y · y · y
Need a hint?
- Count how many x’s are multiplied.
- That count is the exponent.
A2
Write as a single power: x · x · x
Need a hint?
- Count how many x’s are multiplied.
- That count is the exponent.
A3
Write as a single power: 3 · z · z · z · z
Need a hint?
- Count how many x’s are multiplied.
- That count is the exponent.
A4
Write as a single power: 2 · y · y
Need a hint?
- Count how many x’s are multiplied.
- That count is the exponent.
Extension
Extension (4)
E1
Write as a single power: 2 · z · z · z
Need a hint?
- Count how many x’s are multiplied.
- That count is the exponent.
E2
Write as a single power: 3 · x · x · x
Need a hint?
- Count how many x’s are multiplied.
- That count is the exponent.
E3
Write as a single power: x · x · x · x
Need a hint?
- Count how many x’s are multiplied.
- That count is the exponent.
E4
Write as a single power: z · z · z
Need a hint?
- Count how many x’s are multiplied.
- That count is the exponent.