Algebra and Foundations 1

Question 1

Index form

Answer 1

Index form

Question 2

What are the names of the different parts of numbers in index form?

Answer 2

x²

x= the base

2= the index/indices (or in different context called power/exponent.

Question 3

What is the coefficient?

Answer 3

ax²

a = the coefficient. It is always to the left of whatever has been raised to a power.

The can also be secret 1 coefficient: (1)x²

Question 4

What is secret power of 1?

Answer 4

There can be secret power of 1 just like coefficient.

Question 5

What do you do when you multiply numbers in index form?

Answer 5

You add the powers - index law

Base number must be equal.

If bases are not equal, you cannot simplify. You would need to turn it into ordinary form and then simplify.

For why it works, see notebook

Question 6

Dividing numbers in index form?

Answer 6

You subtract the powers.

Base must be equal again.

For why it works, see notebook

Question 7

Raising numbers in index form to a power?

Answer 7

Multiply the powers to get rid of the brackets.

See notebook for why and example

Question 8

When raising to the power of 0?

Answer 8

Anything to the power of 0 = 1

It’s a secret 1

For why, see notebook

Question 9

What is 0 to the power of 0?

Answer 9

Mathematically undefined

Question 10

Fractional powers?

Answer 10

The denominator comes outside the radical symbol.

If there is a coefficient, it comes before the radical symbol.

See notebook for example

Question 11

What to do when negative powers?

Answer 11

If a non-fraction is raised to negative power, then rewrite as fraction with 1 on top, and turn power positive.

If a fraction is raised to negative power, then swap the top & bottom and turn power into positive.

Question 12

What to do when negative fractional powers?

Answer 12

Do the same as fractional powers, and put everything under fraction.

See notebook

Question 13

Multiplying numbers in index form with coefficient

Answer 13

see notebook