Laws of indices

Worksheet: Laws of indices

Name:Class:

Answer the questions.

1. What is 2³ written out as a number?
   a) 5b) 6c) 8d) 9
2. In the expression 5⁴, what is the index?
   a) 20b) 4c) 5d) 9
3. Which is the same as 3 × 3 × 3 × 3 × 3?
   a) 15b) 3 × 5c) 3⁵d) 5³
4. Simplify a³ × a⁴.
   a) 2a⁷b) ac) a¹²d) a⁷
5. Simplify 2⁵ × 2².
   a) 2¹⁰b) 2⁷c) 4¹⁰d) 4⁷
6. Simplify x⁹ ÷ x⁶.
   a) x³b) x¹⁵c) x⁵⁴d) x⁶
7. Simplify 7⁸ ÷ 7³.
   a) 1⁵b) 7²⁴c) 7¹¹d) 7⁵
8. What is the value of 9⁰?
   a) 0b) 1c) 9d) 90
9. What is 10⁴ written as a number?
   a) 10 000b) 100 000c) 1000d) 40
10. Simplify 3y² × 4y³.
    a) 12y⁵b) 12y⁶c) 7y⁵d) 7y⁶
11. 5² × 5³ = 5⁵
    a) Trueb) False
12. Any number raised to the power 0 equals 0.
    a) Trueb) False
13. 10⁶ is the number one million.
    a) Trueb) False
14. Simplify m⁷ ÷ m². Give your answer as a power of m.
15. What is the value of 2⁴ × 2⁰?
16. Write 3 000 as a number multiplied by a power of 10.