some basic laws of indices
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Answer:
Index laws are the rules for simplifying expressions involving powers of the same base number. = ( 3 √ 27)2 = (3)2 = 9. (2) Watch out for powers of negative numbers. For example, (−2)3 = −8 and (−2)4 = 16, so (−x)5 = −x5 and (−x)6 = x6.
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 5.2
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 2.3
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.
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