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Level 3-4 Algebra - Powers
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Level 3-4 Algebra - Powers

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 .
19 is 1. What is 91?
1
9
18
19
2 .
If x = 2 and y = 8, what is the answer to 8y / x4?
2
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)
3 .
111 - x3 = -105. What is the value of x?
3
6
9
12
4 .
To what power does 6 need to be raised to give a value of 216?
2
3
4
5
63 = 6 x 6 x 6
5 .
If a2 = 25, what is the value of a4?
29
50
125
625
a must be 5. a4 therefore must be 5 x 5 x 5 x 5
6 .
Which of these gives the largest value?
4 + 6
4 x 6
46
64
64 = 1,296 whilst 46 = 4,096. We Googled it - did you?
7 .
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
Answer is 729
8 .
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
Experiment with different values for y until you find the correct answer
9 .
If a = 3 and b = 10, what is the difference between a4 and b2?
17
19
21
23
a4 = 3 x 3 x 3 x 3 = 81
10 .
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
3b3 = 3 x 125 = 375
You can find more about this topic by visiting BBC Bitesize - Power and roots

Author:  Frank Evans (Specialist 11 Plus Teacher and Tutor)
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