Indicies

Question 1

Multiplication Law:

Answer 1

When multiplying with any base (same or different), you add the exponents.
Example:

Question 2

Division Law:

Answer 2

When dividing with any base, you minus the exponents.
Example:

Question 3

What does an index/power/exponent look like?

Answer 3

It is the number of times a number or letter below it has been multiplied by itself.

Question 4

What does a base look like?

Answer 4

A base is the big number on the bottom which can have an index or not.

Question 5

What is the rule when there is a Zero Index?

Answer 5

0 always equals 1, so anything to the power of 0 equals 1.

Question 6

Should you ever have decimals in your answer?

Answer 6

No you should NOT have decimals in your answer, always change it to a fraction.

Question 7

What should you do when a question has numbers and letters in one bracket, to the power of something?

Answer 7

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

Question 8

What should you do when multiplying and dividing with the same base?

Answer 8

You keep bases the same and only add or minus the indices.

Question 9

What should you do when there are fractions in a bracket with an index on the outside.

Answer 9

You put each half to the POWER of it, and do it for the numerator and the denominator.

Question 10

What is the Order of Operations?

Answer 10

BIDMAS:
B - Brackets
I - Indices
D - Division
M - Multiplication
A - Addition
S - Subtraction

Question 11

What should you do when the question says EVALUATE?

Answer 11

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

Question 12

What should you do when the question says INDEX FORM?

Answer 12

You should put the finished/answered product. Leave with an index.

Example: 3 x 3 x 3 x 3 x 3 =
3(5)

Question 13

What should you do when the question says BASIC NUMERAL?

Answer 13

You should leave no indices left, just a whole number. Leave as a number answer.

Example: 2(3)2 =
2(6) = 64

Question 14

What should you do when the question says USE YOUR CALCULATOR TO VERIFY THE FOLLOWING?

Answer 14

You should just write down the correct answer, nothing else.

Example: 9(0) = 1 =
1

Question 15

What should you do when the question says EXPANDED FORM?

Answer 15

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

Question 16

What do you do when you have a negative index and it’s on the top of a fraction?

Answer 16

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.

Question 17

What does a negative index mean?

Answer 17

A fraction without the minus, and that the negative index is the numerator.

Question 18

When making a fraction that involves both positive and negative indices, what do you do?

Answer 18

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.

Question 19

What do you do when there are things inside the brackets?

Answer 19

Whenever something is in the brackets, you raise it to a power. You only actually get the number answer if the question says EVALUATE.

Question 20

What do you do when the index has letters in it, and it equals something else?

Answer 20

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 = ?

Question 21

What should you do when the question says SIMPLIFY:

Answer 21

Don’t have negative or fractional indices in your answer.

Question 22

What does the power of 1/2 mean?

Answer 22

Any number raised to the power of 1/2 is the square root of that number.

Question 23

What does the power of 1/3 mean?

Answer 23

Any number raised to the power of 1/3 is the cubed root of that number.

Question 24

What does the power of 1/n mean? (n representing any number)

Answer 24

Any number raised to the power of 1/n is the nth root of that number.