1.4 Welcome to indices! (H/F)

Indices are powers that tell us how many times to multiply something by itself and/or how many times to root it.

There are some nice quick rules we can use for combining indices which will come in great use for the rest of the GCSE course! We will cover:

• Types of power: positive, negative and fractional powers;
• Multiplying numbers with indices; and
• Compound indices.

I hope you enjoy the content!

1.4.1 Types of indices (H/F)

There are three types of indices; powers, reciprocals and roots.

Powers: these tell us how many times to multiply something by itself.

Example:

Reciprocals: these tell us if we need to put a number on the bottom of a fraction. If an indices is positive, we don't need to worry. If an indices is negative then we need to find a reciprocal: a negative power means we have a reciprocal ()

Example:

Roots: these tell us to root a number rather than multiply it by itself. If we have indices that are fractions, it means we have to find a root: roots are found on the bottom of a fraction in the indices.

Examples:

1.4.2 Multiplying numbers with indices (H/F)

To multiply numbers with indices or powers, you could multiply everything out and see what you end up with.

Example:

However, there is a much faster way by following this rule!

Rule: [where a, n and m represent any numbers]

Example:

1.4.3 Compound indices (H/F)

Compound indices when we put a number already to a certain power, to another power.

Example:

Again, here we could multiply everything out properly to see what we end up with.

Example:

However, as before, there is a much faster way using this rule...

Rule: [where a, n and m represent any numbers]

Example:

1.4.4 Test your knowledge!

Here are some graded past paper exam questions on indices.

Have a go with pen and paper to see if you can get to the answers!

If you are taking Foundation Tier, only try the questions graded 3, 4 and 5 unless you feel like a challenge! In the video below I walk through them all in case you get stuck...

Grade 5:

Grade 6:

Grade 6:

Grade 7:

Grade 7: