Simplifying · Powers · E6

Coefficient × power.

Multiply the coefficients AND add the exponents: 3x · 2x = 6x², and 4x² · 2x = 8x³.

01 / THE IDEA

See it simplify.

Watch it simplify

Coefficient × power

3x · 2x: 3·2 = 6, and x·x = x² → 6x².

1 / 1
3x⋅2x3x\cdot 2x
1

Simplify

Multiply out and write it in simplest form.

6x26x^{2}
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.

Two jobs at once

3x · 2x = (3·2)(x·x) = 6x². Numbers multiply; same-base powers add their exponents.

Why it works

Multiply the counts, stack the xs.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

4x · 2x

1

Simplify

Multiply out and write it in simplest form. → 8x^2

EX 2medium

7x · 8x

1

Simplify

Multiply out and write it in simplest form. → 56x^2

EX 3hard

8x · 5x

1

Simplify

Multiply out and write it in simplest form. → 40x^2

04 / COMMON TRAPS

Where students slip.

Trap

3x · 2x = 6x.

Fix

x · x = x²: the answer is 6x².

Trap

3x · 2x = 5x².

Fix

Multiply the coefficients: 6, not 5.

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 4x · 2x

Need a hint?
  • Multiply the numbers in front.
  • Add the exponents (x · x = x²).
C2

Simplify 5x · 5x

Need a hint?
  • Multiply the numbers in front.
  • Add the exponents (x · x = x²).
C3

Simplify 2x · 3x

Need a hint?
  • Multiply the numbers in front.
  • Add the exponents (x · x = x²).
C4

Simplify 5x · 2x

Need a hint?
  • Multiply the numbers in front.
  • Add the exponents (x · x = x²).
Apply

Apply (4)

A1

Simplify 7x · 8x

Need a hint?
  • Multiply the numbers in front.
  • Add the exponents (x · x = x²).
A2

Simplify 3x · 9x

Need a hint?
  • Multiply the numbers in front.
  • Add the exponents (x · x = x²).
A3

Simplify 5x · 6x

Need a hint?
  • Multiply the numbers in front.
  • Add the exponents (x · x = x²).
A4

Simplify 8x · 9x

Need a hint?
  • Multiply the numbers in front.
  • Add the exponents (x · x = x²).
Extension

Extension (4)

E1

Simplify 8x · 5x

Need a hint?
  • Multiply the numbers in front.
  • Add the exponents (x · x = x²).
E2

Simplify 9x · 8x

Need a hint?
  • Multiply the numbers in front.
  • Add the exponents (x · x = x²).
E3

Simplify 10x · 8x

Need a hint?
  • Multiply the numbers in front.
  • Add the exponents (x · x = x²).
E4

Simplify 11x · 7x

Need a hint?
  • Multiply the numbers in front.
  • Add the exponents (x · x = x²).