Indicies Flashcards
Multiplication Law:
When multiplying with any base (same or different), you add the exponents.
Example:
Division Law:
When dividing with any base, you minus the exponents.
Example:
What does an index/power/exponent look like?
It is the number of times a number or letter below it has been multiplied by itself.
What does a base look like?
A base is the big number on the bottom which can have an index or not.
What is the rule when there is a Zero Index?
0 always equals 1, so anything to the power of 0 equals 1.
Should you ever have decimals in your answer?
No you should NOT have decimals in your answer, always change it to a fraction.
What should you do when a question has numbers and letters in one bracket, to the power of something?
First, you do the POWER to whatever is the number base, and put the answer. Then work out all the letters by MULTIPLYING the indices.
Only multiply the base when it’s a numeral and has a letter
What should you do when multiplying and dividing with the same base?
You keep bases the same and only add or minus the indices.
What should you do when there are fractions in a bracket with an index on the outside.
You put each half to the POWER of it, and do it for the numerator and the denominator.
What is the Order of Operations?
BIDMAS:
B - Brackets
I - Indices
D - Division
M - Multiplication
A - Addition
S - Subtraction
What should you do when the question says EVALUATE?
You should answer/solve the question. You should fully evaluate the question, leave no indices left, just a whole number. Leave as a number answer.
Example: 2(5) =
32
What should you do when the question says INDEX FORM?
You should put the finished/answered product. Leave with an index.
Example: 3 x 3 x 3 x 3 x 3 =
3(5)
What should you do when the question says BASIC NUMERAL?
You should leave no indices left, just a whole number. Leave as a number answer.
Example: 2(3)2 =
2(6) = 64
What should you do when the question says USE YOUR CALCULATOR TO VERIFY THE FOLLOWING?
You should just write down the correct answer, nothing else.
Example: 9(0) = 1 =
1
What should you do when the question says EXPANDED FORM?
You should expand the question and write it. Leave it expanded, don’t put it together again.
Example: m(2) x h(3) =
m x m x h x h x h
What do you do when you have a negative index and it’s on the top of a fraction?
You move it to the BOTTOM, and you flip the whole fraction backwards. You then delete the minus sign off the index so the index is then positive.
What does a negative index mean?
A fraction without the minus, and that the negative index is the numerator.
When making a fraction that involves both positive and negative indices, what do you do?
Anything with a positive index stays at the top of the fraction (it’s the numerator), and anything with a negative index stays at the bottom of the fraction (it’s the denominator.
The only exception is that if the negative index is already on the top then you flip it to the bottom.
What do you do when there are things inside the brackets?
Whenever something is in the brackets, you raise it to a power. You only actually get the number answer if the question says EVALUATE.
What do you do when the index has letters in it, and it equals something else?
You make the number without the index a number with an index - to show it’s to the power of that number. If you need to flip the fraction, you can. Now put it in brackets to that index if needed, otherwise flip the number to the opposite side to make it even. Then cross out any like terms to get the index. Have the answer as
x = ?
What should you do when the question says SIMPLIFY:
Don’t have negative or fractional indices in your answer.
What does the power of 1/2 mean?
Any number raised to the power of 1/2 is the square root of that number.
What does the power of 1/3 mean?
Any number raised to the power of 1/3 is the cubed root of that number.
What does the power of 1/n mean? (n representing any number)
Any number raised to the power of 1/n is the nth root of that number.
