what is an maths indices

Law of indices
An index, or power, is the small floating number that appears after numbers or letters.

• For example, in numbers 2^6, 6 is the index of 2.
• Example: 5³ = 5 × 5 × 5 = 125 or 

• In words: 5³ could be called "5 to the third power", "5 to the power 3" or simply "5 cubed"

what happens to + and - numbers of odd and even indices?
Negative number indices with indices that are negative give you a negative.
Examples: (-3)⁹ = (-3) × (-3) × (-3) × (-3) × (-3) × (-3) × (-3) × (-3) × (-3) = -19683
negative number with our even indices give you a positive value.
Examples:(-4)⁶ = (-4) × (-4) × (-4) × (-4) × (-4) × (-4) = 4096

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• what are the rules for indices?

• (read as ' squared') means a × a . has been multiplied by itself twice. The index, or power, here is 2.

• (read as ' cubed') means a × a × a . has been multiplied by itself three times.

• (read as ' to the power of 4') means a × a × a × a . has been multiplied by itself four times, and so on.

what are the rules around multiplying and dividing positive and negative numbers?

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. 

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.