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The three laws of indices, applied one at a time with the law named: multiply and add the powers, divide and subtract them, raise a power to a power and multiply. Small answers are evaluated in full so the index form and the ordinary number sit side by side.

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    Worked Example

    Simplify 2⁴ × 2³ and evaluate it.

    1. Same base multiplied, so ADD the powers:4 + 3 = 7
    2. So 2⁴ × 2³ = 2⁷
    3. Evaluate:2⁷ = 128

    Answer: 2⁷ = 128

    Try These Yourself

    Simplify 5⁸ ÷ 5⁶.Show answerHide answer

    Answer: 5² = 25

    Subtract the powers: 8 − 6 = 2.

    Simplify (3²)³.Show answerHide answer

    Answer: 3⁶ = 729

    Multiply the powers: 2 × 3 = 6.

    What is 7⁰?Show answerHide answer

    Answer: 1

    Anything except 0 to the power 0 is 1.