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Lesson 1 of 2

SHORTCUT

The three power rules

Multiplying adds the powers, dividing subtracts, a power of a power multiplies.

The question

Simplify x⁵ × x³

The trick

Same base, multiplying → add the powers. Same base, dividing → subtract. A bracket raised to a power → multiply the powers.

Worked example

  1. 1x⁵ × x³ has the same base x
  2. 2Multiplying means adding the powers: 5 + 3 = 8
  3. 3So the answer is x⁸

So: x⁸

Remember it like this

Times means plus, divide means minus, bracket means multiply. The operation always steps down one level.

In the exam

The rules only apply when the base is the same — x³ × y² cannot be combined. And remember anything to the power 0 is 1, which examiners slip into longer questions to catch people out.

Why it works

x⁵ is five x's multiplied together and x³ is three more. Put them side by side and you simply have eight x's — the addition is just counting.

Explain this to my childGet the words to teach it, in your language

Try it yourself

0/4 correct
  • 1

    Simplify x⁴ × x⁶ (write as x^n)

  • 2

    Simplify x⁹ ÷ x⁴ (write as x^n)

  • 3

    Simplify (x³)⁴ (write as x^n)

  • 4

    What is x⁰?