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NZAMT NZQA NZ Grapher NZ Maths Census at School Study It

Powers, Roots & Reciprocal

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Powers, Roots, Reciprocal

Evaluating powers and roots of numbers. Calculator use for squared, cubed, higher powers, square root, cube root, higher roots.

Reciprocal of a number, including fractions

Activity
Indices (www.transum.org)

Khan Video Tutorial: Reciprocal | Powers | Powers 2 | Square Root

Class notes | pdf

p333 Ex 23.03

p9, Ex 1.05

NuLake p39, 40, 41, 42, 43

 

Powers

Meaning
We say
Calculator
Answer
4x4x4x4x4 = 45
"4 to the power 5"
45 = 1024
7x7x7x7 = 74
"7 to the power 4 "
74 = 2401
9x9 = 92
"9 squared"
92 = 81
5x5x5 = 53
"5 cubed"
53 = 125

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Roots

 
Meaning
We say
Calculator
Answer
? x ? = 64
Square root of 64
= 8
? x ? x ? = 27
Cube root of 27
or
= 3
?x?x?x?x?=243
Fifth root of 243
or
= 3

 

NOTE: Be careful of using a calculator with negative numbers

-5 squared?
NOT = -25
Correct = 25
-3 to the power of 4
NOT = -81
Correct = 81
Calculator does the power before the negative. BRACKETS enclosing the negative are needed.
 

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Reciprocal

 
Reciprocal of N
The reciprocal is the power of -1
= N-1
Or the result of dividing the number into 1
= 1 N
eg The Reciprocal of 4 = 1/4
 
eg The Reciprocal of 3/5 = 5/3
 
eg The Reciprocal of 0.125 = 8
 

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