1. More Exponent Rules
When you have a power raised to another exponent
(42)4 = 42 x 4 = 48
Keep the base and multiply the exponents
To find out how this works we can look at repeated
multiplication
42 = 4 x 4 so (42)4 = (4 x 4)4
Which is equal to
(4 x 4) x (4 x 4) x (4 x 4) x (4 x 4)
= 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 = 48
In general the rule is
(am)n = am x n
Which reads when a power is raised to an exponent
keep the base and multiply the exponents
Don't get this rule mixed up with
(am)x(an) = am+n
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2. When two numbers that are multiplied are both raise to an
exponent you can apply the exponent to each number.
(­3 x 4)2=(­3)2 x 42
And to find the reason why it works we can look at
repeated multiplication
(­3 x 4)2=(­3 x 4)x(­3 x 4)=(­3) x (­3) x (4) x (4) = (­3)2 x 42
The general rule is
(a x b)n = an x bn
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3. When the base is a fraction which is raised to an exponent you
raise both the numerator and denominator to that exponent
4 43
5 53
and we can see the reason why when we look at repeated
multiplication
4 4 4 4 43
5 5 5 5 53
Our general rule here is
a a
b b
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4. Sometimes you need to use more than one
exponent rule to simplify to a single power.
Make sure to carry out the operations using the
correct order of operations
Example 1
Example 2
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5. Assignment
page 106 questions 14­16
page 107 questions 17­22
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