The Laws of Indices (Junior Cert Mathematics): Flashcards

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The Laws of Indices
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What does an exponent/power tell you?

How many times to multiply a number by itself

In 232^3, identify the base

22

In 232^3, identify the exponent/power

33

Product of Powers law formula

ap×aq=ap+qa^p \times a^q = a^{p+q}

Multiplying powers with same base: what to do with powers?

Add the powers

Quotient of Powers law formula

apaq=apq\frac{a^p}{a^q} = a^{p-q}

Dividing powers with same base: what to do with powers?

Subtract the powers

Power of a Power law formula

(ap)q=ap×q(a^p)^q = a^{p \times q}

Raising a power to another power: what to do with powers?

Multiply the powers together

What must be same for laws of indices to work?

The base

What do negative powers mean?

Take the reciprocal, then apply the positive power

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