LAW 1:
The first law of indices tells us that when multiplying two identical numbers together that have different powers (eg: 2² x 2³), the answer will be the same
number to the power of both exponents added together. In algebraic form, this rule look like this: . The a represents the number and n
and m represent the powers. Here is an example of this rule in action.
Example:
In the example, we have added 2 and 3 together to give us 5. So, the solution is 3 to the power of 5.

LAW 2:
The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In
algebraic form, this rule is as follows . The a represents the number that is divided by itself and m and n represent the powers. Here is an
example for this rule.
Example:
As you can see, the powers have been subtracted (5-3=2). So the solution is 4 to the power of 2.

LAW 3:
The third and last law tells us that when we have to multiply a power in a bracket, by another power outside the bracket, we have to multiply the two powers
together to get the answer. In algebraic form, this rule looks like this . The a represents the number in the bracket while the m and n
represent the two powers (one inside and one outside of the bracket). Here is an example in which this rule is applied.
Example:
In this example, the powers were multiplied together to give the answer which is 3 to the power of 6.

Example 1
In this example, we have 4 to the power
of 3 which is equal to 4 x 4 x 4. The
answer to the problem is 64.

Example 2
In this example, we are working with a
very large power: 6. As a result we have
to use 2 six times in the multiplication.

Example 3
In this example, we have to use 5 four
times in the multiplication which gives
us a very large answer.

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Chapter 7.1: Learning Outcomes
Students will be able to identify and use powers!
Students will know and be able to apply the 3 laws of indices!
Students will know that any number to the power of 0 is 1!

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