Powers · Combine the laws · 7.2

Multi- step.

Harder problems chain the laws: simplify powers of powers first, then multiply or divide, working one rule at a time until the expression is in simplest form.

01 / THE IDEA

See it work.

Watch the method

Multi-step

Apply one rule at a time, simplest form at the end.

1 / 2
x4⋅x2x^{4} \cdot x^{2}
1

Add the exponents

Same base x — keep the base, add the exponents: 4 + 2.

x4⋅x2=x6x^{4} \cdot x^{2} = x^{6}
2

Write the product

Same base when multiplying → add exponents.

x4⋅x2=x6x^{4} \cdot x^{2} = x^{6}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type with ^ for powers — e.g. x^5.

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— / WHY IT WORKS

The idea underneath.

One rule at a time

Resolve brackets/powers first, then multiply and divide, keeping the base and combining exponents at each step.

Why it works

Peel the expression down to one power.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify x^3 · x^5

1

Add the exponents

Same base x — keep the base, add the exponents: 3 + 5. x^3 · x^5 = x^8

2

Write the product

Same base when multiplying → add exponents. x^3 · x^5 = x^8

EX 2medium

Simplify y^4 · y^5

1

Add the exponents

Same base y — keep the base, add the exponents: 4 + 5. y^4 · y^5 = y^9

2

Write the product

Same base when multiplying → add exponents. y^4 · y^5 = y^9

EX 3hard

Simplify y^4 · y^2

1

Add the exponents

Same base y — keep the base, add the exponents: 4 + 2. y^4 · y^2 = y^6

2

Write the product

Same base when multiplying → add exponents. y^4 · y^2 = y^6

04 / COMMON TRAPS

Where students slip.

Trap

Doing everything at once.

Fix

Apply one rule per step.

Trap

Forgetting to finish simplifying.

Fix

Combine until no rule applies.

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 z^2 · z^4

Need a hint?
  • Resolve powers of powers first.
  • Then multiply/divide; combine exponents.
C2

Simplify y^4 · y^4

Need a hint?
  • Resolve powers of powers first.
  • Then multiply/divide; combine exponents.
C3

Simplify z^5 · z^2

Need a hint?
  • Resolve powers of powers first.
  • Then multiply/divide; combine exponents.
C4

Simplify y^5 · y^2

Need a hint?
  • Resolve powers of powers first.
  • Then multiply/divide; combine exponents.
Apply

Apply (4)

A1

Simplify y^2 · y^3

Need a hint?
  • Resolve powers of powers first.
  • Then multiply/divide; combine exponents.
A2

Simplify y^4 · y^3

Need a hint?
  • Resolve powers of powers first.
  • Then multiply/divide; combine exponents.
A3

Simplify x^3 · x^5

Need a hint?
  • Resolve powers of powers first.
  • Then multiply/divide; combine exponents.
A4

Simplify y^3 · y^4

Need a hint?
  • Resolve powers of powers first.
  • Then multiply/divide; combine exponents.
Extension

Extension (4)

E1

Simplify y^5 · y^4

Need a hint?
  • Resolve powers of powers first.
  • Then multiply/divide; combine exponents.
E2

Simplify z^5 · z^2

Need a hint?
  • Resolve powers of powers first.
  • Then multiply/divide; combine exponents.
E3

Simplify z^3 · z^5

Need a hint?
  • Resolve powers of powers first.
  • Then multiply/divide; combine exponents.
E4

Simplify y^4 · y^4

Need a hint?
  • Resolve powers of powers first.
  • Then multiply/divide; combine exponents.