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Higher Mathematics Indices www.maths4scotland.co.uk Next

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

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,

Indices Higher Mathematics Rules of Indices

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

Indices Higher Mathematics 3 times 4 times 7 times

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

Indices Higher Mathematics When multiplying We ADD the indices Generalising

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

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

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

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

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

Indices Higher Mathematics When dividing We SUBTRACT the indices Generalising

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

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

Indices Higher Mathematics 3 times 4 times 4  3 terms

Indices Higher Mathematics m times n times m  n terms

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

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

Indices Higher Mathematics 3 times Recall division

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

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

Indices Higher Mathematics 3 times 2 times Recall division

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

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

Indices Higher Mathematics 3 times 4 times Recall division

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

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

Indices Higher Mathematics 2 times 5 times Recall division

Indices Higher Mathematics m times m +n times Generalising

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

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

Indices Higher Mathematics Recall multiplication ButSo, Hence Thus

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

Indices Higher Mathematics Recall multiplication and, Hence Thus n times

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

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

Indices Higher Mathematics Recall powers Thus So,But,

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

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

Indices Higher Mathematics Recall Then and,

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

Indices Higher Mathematics Rules of Indices Multiplying Dividing Powers

Indices Higher Mathematics Special Indices Power of 0 Power of 1

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

Indices Higher Mathematics More Examples - 1 Simplify

Indices Higher Mathematics More Examples - 2 Simplify

Indices Higher Mathematics More Examples - 3 Multiply out the brackets

Indices Higher Mathematics More Examples - 4 Simplify

Indices Higher Mathematics More Examples - 5 Solve the equation:

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

Indices Higher Mathematics More Examples - 7 Write in root form

Indices Higher Mathematics More Examples - 8 Write in index form

Indices Higher Mathematics More Examples - 9 Evaluate

Indices Higher Mathematics More Examples - 10 Simplify

Indices Higher Mathematics More Examples - 11 Simplify

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