courses › Pre-Algebra

Powers, the rules for combining them, and square roots.

In your head, jot if needed · no calculator why?

Learn first (about 3 minutes)

Opens at level 18.

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Builds on: Factors & primes (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Powers par 6 s not tried yet

  worked example

  7³

  Answer: 343

  1. Start at 1 and multiply by 7, 3 times: 7, 49, 343.

• Square & cube roots par 6 s not tried yet

  worked example

  ∛729

  Answer: 9

  1. 9 × 9 × 9 = 729, so ∛729 = 9.

• Exponent rules par 9 s not tried yet

  worked example

  (x² × x⁵) ÷ x³ = xⁿ. What is n?

  Answer: 4

  1. Multiplying adds exponents: 2 + 5 = 7.
  2. Dividing subtracts: 7 − 3 = 4.

• Simplify a square root par 16 s not tried yet

  worked example

  Write √162 as a√b in simplest form. Enter a, b.

  Answer: (9, 2)

  1. Find the largest square factor: 162 = 81 × 2, and √81 = 9.
  2. So √162 = 9√2, and 2 has no square factor other than 1.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

your rounds

No rounds yet.