Powers · Add & subtract powers · 2.1

Like terms.

Two power-terms are “like” only if they have the SAME base and the SAME exponent. 3x² and 5x² are like; 3x² and 5x³ are not; 3x² and 5y² are not.

01 / THE IDEA

See it work.

Watch the method

Like terms

Like terms match in both base and exponent.

1 / 1
3x2+5x23x^{2} + 5x^{2}
1

Simplify

Apply the exponent laws.

3x2+5x2=8x23x^{2} + 5x^{2} = 8 x^{2}
— / WHY IT WORKS

The idea underneath.

What makes terms alike

Only terms with identical variable parts can be added or subtracted. The coefficient can differ; the base and exponent cannot.

Why it works

x² apples and x³ oranges don’t combine.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Are 6x^3 and 3y^4 like terms (can they be combined)?

1

Check

Compare base and exponent → No.

EX 2medium

Are 3x^3 and 2x^3 like terms (can they be combined)?

1

Check

Compare base and exponent → Yes.

EX 3hard

Are 5y^4 and 3y^4 like terms (can they be combined)?

1

Check

Compare base and exponent → Yes.

04 / COMMON TRAPS

Where students slip.

Trap

Combining x² and x³.

Fix

Different exponents → not like terms.

Trap

Combining x² and y².

Fix

Different bases → not like terms.

05 / QUIZ

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

Are 2x^4 and 4x^4 like terms (can they be combined)?

Need a hint?
  • Check the base AND the exponent.
  • Both must match to combine.
C2

Are 5y^3 and 3x^3 like terms (can they be combined)?

Need a hint?
  • Check the base AND the exponent.
  • Both must match to combine.
C3

Are 2x^2 and 6x^2 like terms (can they be combined)?

Need a hint?
  • Check the base AND the exponent.
  • Both must match to combine.
C4

Are 2y^3 and 6x^3 like terms (can they be combined)?

Need a hint?
  • Check the base AND the exponent.
  • Both must match to combine.
Apply

Apply (4)

A1

Are 5y^2 and 5y^2 like terms (can they be combined)?

Need a hint?
  • Check the base AND the exponent.
  • Both must match to combine.
A2

Are 5y^3 and 5y^3 like terms (can they be combined)?

Need a hint?
  • Check the base AND the exponent.
  • Both must match to combine.
A3

Are 3x^3 and 2y^2 like terms (can they be combined)?

Need a hint?
  • Check the base AND the exponent.
  • Both must match to combine.
A4

Are 4y^3 and 5x^3 like terms (can they be combined)?

Need a hint?
  • Check the base AND the exponent.
  • Both must match to combine.
Extension

Extension (4)

E1

Are 6x^2 and 4x^2 like terms (can they be combined)?

Need a hint?
  • Check the base AND the exponent.
  • Both must match to combine.
E2

Are 6x^3 and 4x^4 like terms (can they be combined)?

Need a hint?
  • Check the base AND the exponent.
  • Both must match to combine.
E3

Are 2y^3 and 6x^3 like terms (can they be combined)?

Need a hint?
  • Check the base AND the exponent.
  • Both must match to combine.
E4

Are 3x^3 and 4x^2 like terms (can they be combined)?

Need a hint?
  • Check the base AND the exponent.
  • Both must match to combine.