Indicies

Question 1

What is an index / indices

Answer 1

A number showing how many times a number is multiplied by itself.

Question 2

How do you solve a number to the negative power e.g 7^-2

Answer 2

First multiply the number the amount of times the power shows
7×7 = 49

Then make it the reciprocal
So your answer is 1/49

Question 3

How do you solve a number whose power is a fraction e.g 4^2/3

Answer 3

First you root the number by the denominator so
Cube root 4 =1.587
Next use the numerator as the power and raise it to the appropriate power

1.587^2 = 2.518

Question 4

How do you solve a number with a negative fraction as its power
E.g 5^-1/2

Answer 4

First get the reciprocal of the number so
1/5^1/2

Then we use the denominator to root the number so
√1/5 = √5/5 = 0.4472

Now use the power to appropriately multiply the fraction

So 0.4472^1 = 0.4472

Question 5

What happens when you multiply two numbers (of the same number) with a power

Answer 5

The powers add

8^4 × 8^2 = 8^6

Question 6

What happens when you divide two numbers (of the same number) with a power

Answer 6

Subtract the powers
5^4 ÷ 5^2 = 5^2

Question 7

Adding and subtracting with powers

Answer 7

The power doesn’t change but the number does - the powers must be the same

7^4 + 2^4 =9^4

Question 8

What happens when you root a power

Answer 8

The power is divided by the root