Simplifying · Powers · E1

What is a power?

A power is repeated multiplication. x · x = x² ("x squared"); x · x · x = x³. The exponent counts how many xs are multiplied — it is NOT 2x.

01 / THE IDEA

See it simplify.

Watch it simplify

What is a power?

x² means x · x; the little 2 counts the factors.

1 / 2
2x2+5x22x^2 + 5x^2
1

Group like terms

Gather the terms that share the same variable part.

(2x2+5x2)(2x^{2} + 5x^{2})
2

Combine

Add the coefficients within each group.

7x27x^{2}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Simplify it.

Type the simplest form (e.g. 6x + 5). Use ^ for powers.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Exponent = count of factors

x² = x · x, x³ = x · x · x. The exponent is how many copies are multiplied. x² is very different from 2x (which is x + x).

Why it works

x² is an x-by-x square; 2x is two x-sticks.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

6x² + 4x²

1

Group like terms

Gather the terms that share the same variable part. → (6x^2 + 4x^2)

2

Combine

Add the coefficients within each group. → 10x^2

EX 2medium

6x² + 7x²

1

Group like terms

Gather the terms that share the same variable part. → (6x^2 + 7x^2)

2

Combine

Add the coefficients within each group. → 13x^2

EX 3hard

9x² + 4x²

1

Group like terms

Gather the terms that share the same variable part. → (9x^2 + 4x^2)

2

Combine

Add the coefficients within each group. → 13x^2

04 / COMMON TRAPS

Where students slip.

Trap

x² = 2x.

Fix

x² = x · x, not x + x.

Trap

x² = x · 2.

Fix

The 2 is an exponent, not a multiplier.

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

Simplify 6x² + 4x²

Need a hint?
  • x² means x times x.
  • The exponent counts factors, not copies added.
C2

Simplify 2x² + 4x²

Need a hint?
  • x² means x times x.
  • The exponent counts factors, not copies added.
C3

Simplify 5x² + 3x²

Need a hint?
  • x² means x times x.
  • The exponent counts factors, not copies added.
C4

Simplify 2x² + 2x²

Need a hint?
  • x² means x times x.
  • The exponent counts factors, not copies added.
Apply

Apply (4)

A1

Simplify 6x² + 7x²

Need a hint?
  • x² means x times x.
  • The exponent counts factors, not copies added.
A2

Simplify 7x² + 9x²

Need a hint?
  • x² means x times x.
  • The exponent counts factors, not copies added.
A3

Simplify 9x² + 6x²

Need a hint?
  • x² means x times x.
  • The exponent counts factors, not copies added.
A4

Simplify 8x² + 9x²

Need a hint?
  • x² means x times x.
  • The exponent counts factors, not copies added.
Extension

Extension (4)

E1

Simplify 9x² + 4x²

Need a hint?
  • x² means x times x.
  • The exponent counts factors, not copies added.
E2

Simplify 9x² + 12x²

Need a hint?
  • x² means x times x.
  • The exponent counts factors, not copies added.
E3

Simplify 5x² + 11x²

Need a hint?
  • x² means x times x.
  • The exponent counts factors, not copies added.
E4

Simplify 10x² + 6x²

Need a hint?
  • x² means x times x.
  • The exponent counts factors, not copies added.