Exponents and Roots Flashcards
Free exponents and roots flashcards covering exponent rules, negative and zero exponents, square roots, cube roots, radicals and scientific notation. Flip each card, say the answer first, then mark what you know and drill what you miss.
Type the problems from this lesson and check each step.
How to study with these exponents and roots flashcards
- Read the front of the card and say or write your answer before you flip it.
- Flip the card, then mark I know this only if you were right without hesitating.
- Mark Review again for anything you missed, then use Review missed only to drill those cards.
- Pick one topic at a time, then shuffle all topics for a mixed review.
Study tips for exponents and roots
Do short rounds of 10 to 15 cards. Say the answer out loud before you flip, then use Review missed only until the pile is empty. Come back the next day: spacing your practice beats one long session.
All 37 cards at a glance
Every card is also listed below so you can scan, print or review without the viewer.
Exponent rules
| Question | Answer |
|---|---|
| What does 5³ mean | 5 × 5 × 5 = 125. |
| What is the product rule | aᵐ × aⁿ = aᵐ⁺ⁿ. |
| What is the quotient rule | aᵐ / aⁿ = aᵐ⁻ⁿ. |
| What is the power rule | (aᵐ)ⁿ = aᵐⁿ. |
| What is a⁰ for a ≠ 0 | 1. |
| What is a⁻ⁿ | 1 / aⁿ. |
| What is 2⁻³ | 1/8. |
| What is (ab)ⁿ | aⁿbⁿ. |
| What is (a/b)ⁿ | aⁿ / bⁿ. |
| Simplify x⁴ · x⁵ | x⁹. |
| Simplify (x³)² | x⁶. |
| Simplify x⁷ / x² | x⁵. |
| Is (−2)² the same as −2² | No. (−2)² = 4 but −2² = −4. |
| What is the value of 1ⁿ | 1. |
Square roots and cube roots
| Question | Answer |
|---|---|
| What is a square root | A number that multiplies by itself to give the original. √49 = 7. |
| List the perfect squares from 1 to 15 squared | 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. |
| List the first five perfect cubes | 1, 8, 27, 64, 125. |
| What is ∛64 | 4. |
| What is √2 approximately | 1.414. |
| What is √3 approximately | 1.732. |
| Is √2 rational | No, it is irrational: its decimal never ends or repeats. |
| Simplify √50 | 5√2. |
| Simplify √72 | 6√2. |
| What is √a × √b | √(ab). |
| What is √a / √b | √(a/b) for b > 0. |
| What is a radical | An expression using the root symbol √. |
| How do you write a square root as an exponent | √a = a^(1/2). |
| What is the square root of −1 | It is not a real number. It is the imaginary unit i. |
Scientific notation
| Question | Answer |
|---|---|
| What is scientific notation | A number written as a × 10ⁿ with 1 ≤ a < 10. |
| Write 6,500 in scientific notation | 6.5 × 10³. |
| Write 0.0042 in scientific notation | 4.2 × 10⁻³. |
| Write 3 × 10⁴ in standard form | 30,000. |
| What does a negative exponent in scientific notation mean | A number smaller than 1. |
| Multiply (2 × 10³)(3 × 10⁴) | 6 × 10⁷. |
| Divide (8 × 10⁶) / (2 × 10²) | 4 × 10⁴. |
| What is 10⁶ called | One million. |
| What is 10⁹ called | One billion. |
Frequently asked questions
What is the rule for multiplying exponents?
When the bases are the same, add the exponents: x³ × x⁴ = x⁷.
Why is any number to the power 0 equal to 1?
Dividing aⁿ by aⁿ gives 1, and the quotient rule gives aⁿ⁻ⁿ = a⁰, so a⁰ must equal 1 (for a not zero).
How do you simplify a square root?
Pull out the largest perfect-square factor: √50 = √(25 × 2) = 5√2.
Sources
More free math flashcards
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