Powers and Indices

Q: What does "indices" mean in BIDMAS?

In BIDMAS, indices are the powers in a calculation, such as squares and cubes. BIDMAS tells you to work them out right after brackets, and before multiplication, division, addition and subtraction. So in 2 × 5², you square the 5 first, and then multiply.

Q: Why can't you swap the base and the exponent?

Swapping them changes the result, because the base and the exponent do different jobs. The base is the number you multiply, while the exponent counts how many times you use it. If you swap them, you multiply a different number a different number of times, so the answer is no longer the same.

Q: What does a number to the power of 0 equal?

Any number except 0 raised to the power of 0 equals 1. This is a special rule worth remembering, because it often surprises people when they first meet it. The one exception is 0 to the power of 0, which is undefined, meaning it has no single agreed value.

Q: What are square numbers and cube numbers?

Square numbers come from raising a whole number to the power of 2, giving 1, 4, 9, 16, 25 and so on. Cube numbers come from raising a whole number to the power of 3, giving 1, 8, 27, 64 and so on. You can say "squared" and "cubed" for short.

Q: Why does (2 × 5)² give a different answer to 2 × 5²?

The brackets change the order of operations. In (2 × 5)², you work out the brackets first to get 10, and then square it to reach 100. In 2 × 5², there are no brackets, so you square the 5 first to get 25, and then multiply by 2 to reach 50.

Key concept

Powers and indices are a short way to write repeated multiplication of the same number. For example, 2³ = 2 × 2 × 2 = 8. Each power has a base (the number multiplied) and an exponent showing how many times.

Powers and Indices - introduction visual

Video Lesson

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$Powers and Indices poster$

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Flashcards

Review key concepts visually

Introduction to powers by showing the relationship that 3+3+3+3 equals 4 times 3, and 3 × 3 × 3 × 3 equals 3 to the power of 4.

Explanation of the base 3 and index 4 in 3^4 that it is pronounced 'three to the power of four'.

Explaining key characteristics of powers, e.g., 3⁴ is not the same as 4³, a¹ is a, and for a different to 0, a⁰ is 1.

Common indices chart showing square and cube numbers with examples. For example, square numbers 1, 4, 9, 16, and cube numbers 1, 8, 27, 64, 125.

Cartoon blue bird explaining how to simplify 4 × 3 × 3 × 4 × 4 to 4³ × 3² using commutative and associative laws.

BIDMAS calculation rules with indices shown by comparing (2 × 5)^2 and 2 × 5^2, resulting in 100 and 50 respectively.

What are Powers?

Powers show repeated multiplication of the same number.
For example, 3⁴ means 3 × 3 × 3 × 3.

Practice Questions

Test your understanding

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Q1Easy

What is the result of 10⁰?

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Interactive Activity

Practice grouping factors to create exponent expressions

Students Also Ask

The questions students bump into most on this topic

Are powers the same as exponents?

Not quite. A power is the whole expression, made of two parts: a base and an exponent. The exponent is the small raised number that tells you how many times to multiply the base by itself. So the exponent is one part of a power, not another word for the same thing.

What does "indices" mean in BIDMAS?

In BIDMAS, indices are the powers in a calculation, such as squares and cubes. BIDMAS tells you to work them out right after brackets, and before multiplication, division, addition and subtraction. So in 2 × 5², you square the 5 first, and then multiply.

Why can't you swap the base and the exponent?

Swapping them changes the result, because the base and the exponent do different jobs. The base is the number you multiply, while the exponent counts how many times you use it. If you swap them, you multiply a different number a different number of times, so the answer is no longer the same.

What does a number to the power of 0 equal?

Any number except 0 raised to the power of 0 equals 1. This is a special rule worth remembering, because it often surprises people when they first meet it. The one exception is 0 to the power of 0, which is undefined, meaning it has no single agreed value.

What are square numbers and cube numbers?

Square numbers come from raising a whole number to the power of 2, giving 1, 4, 9, 16, 25 and so on. Cube numbers come from raising a whole number to the power of 3, giving 1, 8, 27, 64 and so on. You can say "squared" and "cubed" for short.

Why does (2 × 5)² give a different answer to 2 × 5²?

The brackets change the order of operations. In (2 × 5)², you work out the brackets first to get 10, and then square it to reach 100. In 2 × 5², there are no brackets, so you square the 5 first to get 25, and then multiply by 2 to reach 50.

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