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Write down the index law for .
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Write down the index law for .
The index law is: .
You add the powers when multiplying two powers with the same base.
E.g. .
Write down the index law for .
The index law is: .
You subtract the powers when dividing two powers with the same base.
E.g. .
Write down the index law for .
The index law is: .
You multiply the powers when raising to the power .
E.g. .
Write down the index law for .
The index law is: .
A fractional power of means the root.
E.g. .
Write down the index law for .
The index law is: .
The power outside acts on every term inside, when the terms inside are multiplied together.
E.g. .
Write down the index law for .
The index law is: .
A negative power means 1 over the positive power.
E.g. .
Write down the index law for .
The index law is: .
Anything to the power 1 is itself.
E.g. .
Write down the index law for .
The index law is: .
Anything to the power 0 is 1.
E.g. .
True or False?
False.
The order of and are incorrect.
The correct index law is .
E.g. .
True or False?
can be thought of in two different ways, using powers and roots.
True.
You can swap the order of the root and the power of .
So is the first way to think about it, and is the second way to think about it.
E.g. .
When talking about indices, what is the base?
The base is the number or letter being acted on by the power.
For example, in , the base is and the power is .
What is the first step to solving the equation ?
You need both sides to be over the same base.
So the first step is to change the base of 27 to 3, using the fact 27 = 33.
(Alternatively, you could change the base of 3 to 27, as ).
True or False?
True.
A fraction to a negative power is the same as the flipped fraction to the positive power, .
This is a great trick to use in exams!