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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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SECTION 1.4 EXPONENTS. PRODUCT OF POWERS When you multiply two factors having the same base, keep the common base and add the exponents.

SECTION 1.4 EXPONENTS. PRODUCT OF POWERS When you multiply two factors having the same base, keep the common base and add the exponents.

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