Simplifying · Powers · E5

Multiply, add exponents.

When you multiply powers of the same base, ADD the exponents: x · x² = x³, x² · x³ = x⁵. (You add because you are stacking up factors.)

01 / THE IDEA

See it simplify.

Watch it simplify

Multiply, add exponents

x² · x³ = x⁵ — count all the factors: 2 + 3.

1 / 1
x2⋅x3x^2\cdot x^3
1

Simplify

Multiply out and write it in simplest form.

x5x^{5}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Simplify it.

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

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… =
— / WHY IT WORKS

The idea underneath.

Stacking factors

x² · x³ = (x·x)(x·x·x) = x⁵. Multiplying the same base adds the exponents. This is the opposite of combining like terms (which adds coefficients).

Why it works

Two xs times three xs is five xs multiplied.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

x³ · x³

1

Simplify

Multiply out and write it in simplest form. → x^6

EX 2medium

x³ · x^1

1

Simplify

Multiply out and write it in simplest form. → x^4

EX 3hard

x^1 · x³

1

Simplify

Multiply out and write it in simplest form. → x^4

04 / COMMON TRAPS

Where students slip.

Trap

x² · x³ = x⁶.

Fix

Add the exponents, not multiply: x⁵.

Trap

x² · x³ = x⁵... but writing 2x⁵.

Fix

No new coefficient appears: just x⁵.

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 x³ · x³

Need a hint?
  • Add the exponents.
  • The base stays the same.
C2

Simplify x^1 · x²

Need a hint?
  • Add the exponents.
  • The base stays the same.
C3

Simplify x³ · x²

Need a hint?
  • Add the exponents.
  • The base stays the same.
C4

Simplify x^1 · x³

Need a hint?
  • Add the exponents.
  • The base stays the same.
Apply

Apply (4)

A1

Simplify x³ · x^1

Need a hint?
  • Add the exponents.
  • The base stays the same.
A2

Simplify x³ · x³

Need a hint?
  • Add the exponents.
  • The base stays the same.
A3

Simplify x² · x²

Need a hint?
  • Add the exponents.
  • The base stays the same.
A4

Simplify x² · x^1

Need a hint?
  • Add the exponents.
  • The base stays the same.
Extension

Extension (4)

E1

Simplify x^1 · x³

Need a hint?
  • Add the exponents.
  • The base stays the same.
E2

Simplify x^1 · x²

Need a hint?
  • Add the exponents.
  • The base stays the same.
E3

Simplify x² · x^1

Need a hint?
  • Add the exponents.
  • The base stays the same.
E4

Simplify x^1 · x^1

Need a hint?
  • Add the exponents.
  • The base stays the same.