This is a comprehensive pack of notes about grade 9 expoments. It teaches about exponents, exponential laws, negative exponents, exponential equations and scientific notation. It contains notes, examples and particularly exercises with answers.
Exponents are used to representEXPONENTS
repeated multiplication.
Terminology:
>2x2<
345
Co-efficient exponent
base exponent
CO-efficient is 1 base
Basic concepts of
exponents
Examples
1. Express the following inexponential form:
a) a. a. a. a. a
b) 3m. 3m. 3m
= (3m)3 or 33m3
c) 4x.x. x. X
= 4x4
2. Expand the following:
a) (-1)3
=(-1)(-1)(-1)
=-1
b) (-1)11
= (-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)
=-1
c) (-1)14
=(-1)(-1)(-1) (-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1)(-1(-1)
=+1
d) (-2)*
= (-2)(-2)(-2)(-2)
= +24
= 16
42 | P age
, Fom i s e exDles we can see
that:
= +1
(-1)0dd number = -1
(-a)en nurber = +geven number
(-a)odd number aodd number
Exponential Laws > ONLY for x and+
Exponetial Law 1: Multiplication with the same bases
When we multiply powers with the same base:
Multiply any coefficients
Add the exponents; the bases stay the
same
Example: 2x3 x 4x5
=2 x 4x3+5
=8x8
ExponentialLaw 2: Division with the same
bases
When we divide powers with the
o Divide any same base:
coefficients
o Subtract the
exponents; the bases stay the same
21a4
Example: 7a a # 0
= 21 7at-1
= 3a3
bponestial Lom 3: Raising a power to a
7 When power
raising a power to a power:
Muttiply the exponents
Remember the base stays the SAME
Example 1: (**)s
x3 x5
x15
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