Solving Equations with Indices (Junior Cert Mathematics): Flashcards

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Solving Equations with Indices
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What does an index tell you?

How many times to multiply a number by itself

In 232^3, what is the base?

22

In 232^3, what is the index?

33

Law 1: Multiplying powers with same base

ap×aq=ap+qa^p \times a^q = a^{p+q}

Law 2: Dividing powers with same base

ap÷aq=apqa^p \div a^q = a^{p-q}

Law 3: Power of a power

(ap)q=apq(a^p)^q = a^{pq}

If ax=aya^x = a^y, what can you conclude?

x=yx = y

Calculate 323^2

99

Calculate 232^3

88

Simplify 23×222^3 \times 2^2 using Law 1

25=322^5 = 32

Simplify 54÷525^4 \div 5^2 using Law 2

52=255^2 = 25

Simplify (32)3(3^2)^3 using Law 3

36=7293^6 = 729

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