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Maths Quiz - Level 3-4 Algebra - Powers (Questions)

Understand powers and indices in KS3 algebra. Learn the laws of exponents, simplify expressions with the same base, and use negative and zero indices with confidence.

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Fascinating Fact:

When you multiply powers with the same base, you add the indices. For example, x2 × x3 = x5.

In KS3 Maths, powers (also called indices or exponents) show repeated multiplication. You’ll apply index laws to simplify expressions: add indices when multiplying like bases, subtract when dividing, and handle zero or negative indices correctly.

Key Terms

  • Base: The repeated factor in a power; e.g., in x3 the base is x.
  • Index (Exponent): The small number that tells how many times the base multiplies itself; e.g., the 3 in x3.
  • Power: The whole expression with base and index, such as x3 or 24.

Frequently Asked Questions (Click to see answers)

What are the index laws in KS3 maths?

Same base multiply → add indices: am × an = am+n. Same base divide → subtract indices: am ÷ an = am-n. Power of a power → multiply indices: (am)n = amn. Zero index: a0 = 1 for a ≠ 0.

How do I divide powers with the same base?

Subtract the indices: am ÷ an = am−n (for a ≠ 0). Example: x7 ÷ x3 = x4.

What does a negative index mean?

A negative index gives a reciprocal: x−n = 1/ xn (for x ≠ 0). It doesn’t make the value negative; it flips the power.

Try These Related Quizzes

1. How would you work out the value of 36?
[ ] 3 + 6
[ ] 6 + 3
[ ] 3 x 6
[ ] 3 x 3 x 3 x 3 x 3 x 3
2. 19 is 1. What is 91?
[ ] 1
[ ] 9
[ ] 18
[ ] 19
3. To what power does 6 need to be raised to give a value of 216?
[ ] 2
[ ] 3
[ ] 4
[ ] 5
4. Which of these gives the largest value?
[ ] 4 + 6
[ ] 4 x 6
[ ] 46
[ ] 64
5. If a = 4 and b = 5, which of these is the largest value?
[ ] 4a2
[ ] 3b3
[ ] a + a + a + a
[ ] b + b + b + b + b + b + b + b + b + b + b + b
6. If a = 3 and b = 10, what is the difference between a4 and b2?
[ ] 17
[ ] 19
[ ] 21
[ ] 23
7. In the equation x3 + y2 - 6 = 51, we are told that the value of x is 2. What is the value of y?
[ ] 7 or -7
[ ] 8 or -8
[ ] 9 or -9
[ ] 11 or -11
8. If x = 2 and y = 8, what is the answer to 8y / x4?
[ ] 2
[ ] 4
[ ] 8
[ ] 16
9. If a2 = 25, what is the value of a4?
[ ] 29
[ ] 50
[ ] 125
[ ] 625
10. 111 - x3 = -105. What is the value of x?
[ ] 3
[ ] 6
[ ] 9
[ ] 12

You can find more about this topic by visiting BBC Bitesize - Power and roots

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Maths Quiz - Level 3-4 Algebra - Powers (Answers)
1. How would you work out the value of 36?
[ ] 3 + 6
[ ] 6 + 3
[ ] 3 x 6
[x] 3 x 3 x 3 x 3 x 3 x 3
Answer is 729
2. 19 is 1. What is 91?
[ ] 1
[x] 9
[ ] 18
[ ] 19
3. To what power does 6 need to be raised to give a value of 216?
[ ] 2
[x] 3
[ ] 4
[ ] 5
63 = 6 x 6 x 6
4. Which of these gives the largest value?
[ ] 4 + 6
[ ] 4 x 6
[x] 46
[ ] 64
64 = 1,296 whilst 46 = 4,096. We Googled it - did you?
5. If a = 4 and b = 5, which of these is the largest value?
[ ] 4a2
[x] 3b3
[ ] a + a + a + a
[ ] b + b + b + b + b + b + b + b + b + b + b + b
3b3 = 3 x 125 = 375
6. If a = 3 and b = 10, what is the difference between a4 and b2?
[ ] 17
[x] 19
[ ] 21
[ ] 23
a4 = 3 x 3 x 3 x 3 = 81
7. In the equation x3 + y2 - 6 = 51, we are told that the value of x is 2. What is the value of y?
[x] 7 or -7
[ ] 8 or -8
[ ] 9 or -9
[ ] 11 or -11
Experiment with different values for y until you find the correct answer
8. If x = 2 and y = 8, what is the answer to 8y / x4?
[ ] 2
[x] 4
[ ] 8
[ ] 16
Be careful not to mix up multiplying numbers together (as in 8y) when finding the value of numbers with powers (as in 24)
9. If a2 = 25, what is the value of a4?
[ ] 29
[ ] 50
[ ] 125
[x] 625
a must be 5. a4 therefore must be 5 x 5 x 5 x 5
10. 111 - x3 = -105. What is the value of x?
[ ] 3
[x] 6
[ ] 9
[ ] 12
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