Powers, Roots and Standard Form

What this unit covers

This unit page brings together three linked ideas: powers (also called indices or exponents), roots and radicals, and standard form, also called scientific notation. The resources were made by GoConqr users, and every one is free to open and study with no account.

Where to start

Begin with the rules. The Laws Of Indices mind map sets out the first laws: to multiply expressions with the same base, copy the base and add the indices, and to divide, subtract them. The Unit 5 - Exponents and Radicals mind map goes a step further, with negative exponents, an exponent equal to 0 and radical skills.

Then test yourself with the Pre-Test on Powers of 10. It asks you to rewrite numbers as powers of 10 and to read powers of 10 in expanded form.

Roots, surds and standard form

Once the rules feel familiar, move to roots. The Surds mind map shows how to split a root, for example the square root of 8 as the square root of 4 times the square root of 2. The Radicals mind map covers simplifying with a factor tree, then adding and subtracting. Several Radicals flashcard decks give worked simplifications you can practice on.

For standard form, the note on multiplying and dividing standard form works through an example: multiply the numbers, then add the powers of 10. There are also many notes and quizzes on scientific notation to repeat the method.

Using quizzes and maps together

1. Read a mind map on one rule or method.
2. Take a quiz on the same idea, such as Exponents or Standard Form.
3. Note which questions you missed.
4. Go back to the map or a flashcard deck for just those points.

Teachers can use the same order to set a short sequence: a map to introduce, a quiz to check.

Where this unit fits

This unit sits in the Number strand of Mathematics. Some resources mention GCSE Maths and A-level Maths, so you will find material at more than one stage of school.

Ready to begin? Open a mind map you like, then try a quiz and see which ideas need another look.