Laws of indices
An index, or power, is the small floating number that appears after a number or letter. Indices show how many times a number or letter has been multiplied by itself. Index (indices) in Maths is the power or exponent which is raised to a number or a variable.
For example, in number 2^4, 4 is the index of 2.
Example
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23 = 2 × 2 × 2 = 8 In the example, 2 is the base, and 3 is the index.
2^5 means that you have to multiply 2 by itself five times = 2×2×2×2×2 = 32.
There are a number of important rules of index numbers: ya × yb = y.
what are the rules around multiplying positive and negative numbers?
Multiplication and Division of Integers
MULTIPLICATION RULE 1:
The product of a positive integer and a negative integer is negative.
RULE 2:
The product of two positive integers is positive.
RULE 3:
The product of two negative integers is positive.
Examples:
Rule 1: 1. (+4) x (-2) = -8 2. (-2) x (+5) = -10
Rule 2: 1. (+6) x (+8) = +48 2. (+6) x (+2) = +12
Rule 3: 1. (-6) x (-8) = +48 2. (-2) x (-4) = +8
DIVISION RULE 1:
The quotient of a positive integer and a negative integer is negative.
RULE 2: The quotient of two positive integers is positive.
RULE 3: The quotient of two negative integers is positive.
Examples:
Rule 1:
1. (-8) / (+4) = -2 2. (-12) / (+6) = -2
Rule 2:
1. (+6) / (-3) = -2 2. (+24) / (-6) = -4
Rule 3.
1. (+9) / (+3) = +3 2. (+16) / (+4) = +4
Rule 4:
1. (-6) / (-2) = +3 2. (-42) / (-7) = +6
SUMMARY OF MULTIPLICATION AND DIVISION RULES
If the signs are different the answer is negative. If the signs are alike the answer is positive.
