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

How do I divide powers with the same base?

Subtract the indices: a^m ÷ aⁿ = a^m−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 .

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?

2 .

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

3 .

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

4 .

1⁹ is 1. What is 9¹?

5 .

If a² = 25, what is the value of a⁴?

125

625

a must be 5. a⁴ therefore must be 5 x 5 x 5 x 5

6 .

To what power does 6 need to be raised to give a value of 216?

⁴

⁵

6³ = 6 x 6 x 6

7 .

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

8 .

If a = 3 and b = 10, what is the difference between a⁴ and b²?

a⁴ = 3 x 3 x 3 x 3 = 81

9 .

111 - x³ = -105. What is the value of x?

10 .

If x = 2 and y = 8, what is the answer to 8y / x⁴?

Be careful not to mix up multiplying numbers together (as in 8y) when finding the value of numbers with powers (as in 2⁴)

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

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