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Higher Mathematics Indices www.maths4scotland.co.uk Next

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Indices Higher Mathematics What are Indices Indices are a mathematical shorthand If, we have: We can say that this is: 3 multiplied by itself 5 times We write this as: pronounced 3 to the power 5 3 is the BASE 5 is the POWER or INDEX

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Indices Higher Mathematics What are Indices The plural of INDEX is is written in INDEX form also known as power form or power notation INDICES So,

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Indices Higher Mathematics Rules of Indices

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Indices Higher Mathematics Rules of Indices Consider the following What can we make of it ? Can we generalise to make a rule ?

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Indices Higher Mathematics 3 times 4 times 7 times

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Indices Higher Mathematics m times n times m + n times Generalising

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Indices Higher Mathematics When multiplying We ADD the indices Generalising

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Indices Higher Mathematics Examples Remember – to MULTIPLY you ADD the indices

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Indices Higher Mathematics Rules of Indices Consider the following What can we make of it ? Can we generalise to make a rule ?

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Indices Higher Mathematics 5 times 2 times 2 terms on the bottom will cancel out 2 terms on the top

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Indices Higher Mathematics 5 times 2 times 5 - 2 terms 2 terms on the bottom will cancel out 2 terms on the top

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Indices Higher Mathematics m times n times m - n terms n terms on the bottom will cancel out n terms on the top Generalising

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Indices Higher Mathematics When dividing We SUBTRACT the indices Generalising

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Indices Higher Mathematics Examples Remember – to DIVIDE you SUBTRACT the indices

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Indices Higher Mathematics Rules of Indices Consider the following What can we make of it ? Can we generalise to make a rule ?

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Indices Higher Mathematics 3 times 4 times 4 3 terms

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Indices Higher Mathematics m times n times m n terms

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Indices Higher Mathematics Examples Remember – for POWERS you MULTIPLY the indices

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Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

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Indices Higher Mathematics 3 times Recall division

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Indices Higher Mathematics Examples Remember – anything to the power of 0 is 1

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Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

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Indices Higher Mathematics 3 times 2 times Recall division

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Indices Higher Mathematics Examples Remember – anything to the power of 1 is itself

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Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

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Indices Higher Mathematics 3 times 4 times Recall division

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Indices Higher Mathematics Rules of Indices a ‘minus’ index means ‘1 over’ A useful way of remembering this

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Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

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Indices Higher Mathematics 2 times 5 times Recall division

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Indices Higher Mathematics m times m +n times Generalising

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Indices Higher Mathematics Examples Remember – minus means 1 over Express in positive index form

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Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

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Indices Higher Mathematics Recall multiplication ButSo, Hence Thus

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Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

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Indices Higher Mathematics Recall multiplication and, Hence Thus n times

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Indices Higher Mathematics Examples Remember – fraction denominator gives the root Express in root form

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Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

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Indices Higher Mathematics Recall powers Thus So,But,

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Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? Finally, what meaning can we give to

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Indices Higher Mathematics Examples Remember – fraction denominator gives the root Express in root form Remember – fraction numerator gives the power

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Indices Higher Mathematics Recall Then and,

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Indices Higher Mathematics Examples Express in root form Remember – minus means 1 over

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Indices Higher Mathematics Rules of Indices Multiplying Dividing Powers

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Indices Higher Mathematics Special Indices Power of 0 Power of 1

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Indices Higher Mathematics Negative and Fractional Indices Negative Fraction Negative fraction minus means ‘1 over’

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Indices Higher Mathematics More Examples - 1 Simplify

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Indices Higher Mathematics More Examples - 2 Simplify

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Indices Higher Mathematics More Examples - 3 Multiply out the brackets

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Indices Higher Mathematics More Examples - 4 Simplify

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Indices Higher Mathematics More Examples - 5 Solve the equation:

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Indices Higher Mathematics More Examples - 6 Simplify and express in positive index form

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Indices Higher Mathematics More Examples - 7 Write in root form

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Indices Higher Mathematics More Examples - 8 Write in index form

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Indices Higher Mathematics More Examples - 9 Evaluate

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Indices Higher Mathematics More Examples - 10 Simplify

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Indices Higher Mathematics More Examples - 11 Simplify

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Quit C P D www.maths4scotland.co.uk © CPD 2004

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THE END

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