# Laws of indices

> Grade 8: index notation, multiply powers: add the indices, divide powers: subtract the indices, any number to the power 0 is 1, powers of 10.

Source: https://olyclass.com/library/math-g8-indices-en/

- Subject: Math
- Level: Grade 8
- Practice: 16
- Play it free on one screen (projector, TV or whiteboard): https://olyclass.com/library?play=math-g8-indices-en
- Copy and edit it: https://olyclass.com/library?copy=math-g8-indices-en
- Games it plays well in: [Ring the Bell](https://olyclass.com/classroom-games/ring-the-bell/), [High Water](https://olyclass.com/classroom-games/high-water/), [Tug of War](https://olyclass.com/classroom-games/tug-of-war/), [Lucky Wheel](https://olyclass.com/classroom-games/lucky-wheel/)

## Questions

1. What is 2³ written out as a number? (5 / 6 / 8 / 9)
   Answer: 8
2. In the expression 5⁴, what is the index? (20 / 4 / 5 / 9)
   Answer: 4
3. Which is the same as 3 × 3 × 3 × 3 × 3? (15 / 3 × 5 / 3⁵ / 5³)
   Answer: 3⁵
4. Simplify a³ × a⁴. (2a⁷ / a / a¹² / a⁷)
   Answer: a⁷
5. Simplify 2⁵ × 2². (2¹⁰ / 2⁷ / 4¹⁰ / 4⁷)
   Answer: 2⁷
6. Simplify x⁹ ÷ x⁶. (x³ / x¹⁵ / x⁵⁴ / x⁶)
   Answer: x³
7. Simplify 7⁸ ÷ 7³. (1⁵ / 7²⁴ / 7¹¹ / 7⁵)
   Answer: 7⁵
8. What is the value of 9⁰? (0 / 1 / 9 / 90)
   Answer: 1
9. What is 10⁴ written as a number? (10 000 / 100 000 / 1000 / 40)
   Answer: 10 000
10. Simplify 3y² × 4y³. (12y⁵ / 12y⁶ / 7y⁵ / 7y⁶)
   Answer: 12y⁵
11. 5² × 5³ = 5⁵
   Answer: True
12. Any number raised to the power 0 equals 0.
   Answer: False
13. 10⁶ is the number one million.
   Answer: True
14. Simplify m⁷ ÷ m². Give your answer as a power of m.
   Answer: m⁵
15. What is the value of 2⁴ × 2⁰?
   Answer: 16
16. Write 3 000 as a number multiplied by a power of 10.
   Answer: 3 × 10³