Lesson 13 of 14
Track quiz
Show on a big screenTen ideas, ten checks. The table is here to help you.
| Idea | How it goes |
|---|---|
| Base and exponent | The base is the number you multiply. The exponent counts how many. 2⁵ = 32. |
| Counts add | The counts add. The base stays. 2³ × 2⁴ = 2⁷. |
| Counts subtract | The counts subtract. The base stays. 3⁵ ÷ 3² = 3³. |
| Counts multiply | A power of a power multiplies the exponents. (2³)² = 2⁶. |
| Zero count | Each step down the ladder divides by the base. 10⁰ = 1. |
| Ten's columns | Every place-value column is a power of ten. Ones are 10⁰. |
| Standard form | Take a whole number of 10 or more. The exponent counts the digits after the first. |
| Which is larger | Same base above 1? The bigger count wins. Same count above 0? The bigger base wins. Neither the same? Work both out. |
| Below zero | Each step down divides by the base. A count of −2 divides 1 by the base twice. |
| Small numbers | Move the point right. Stop when x is from 1 to below 10. If it moved k places, the exponent is −k. |
A draw halves 32 teams each round. Five rounds leave one team. Which writing shows 32?
Write 3² × 3⁴ as one power.
Write 2⁶ ÷ 2² as one power.
Write (5²)³ as one power of 5.
What is 7⁰?
In 4,073, the digit 4 is worth what?
A made-up sack holds 45,00,000 grains. Which is the standard form?
Which is larger, 2¹⁰ or 10³?
What is 2⁻³?
A made-up bacterium is 0.0000047 m long. What is its length in standard form?
Chapter 2 of Part I is Power Play. You have counted, cancelled and walked a ladder down.
Next: A Story of Numbers. It looks at how ways of writing numbers changed over time.
Reveal every answer to finish this lesson.