Index Laws

Question 1

What does anything to the power of 0 equal?

Answer 1

Any number to the power of 0 equals 1

Question 2

What does anything to the power of 1 equal?

Answer 2

Any number to the power of one equals it self.

Question 3

Fully simplify: g^6 ÷ g^2

Answer 3

g^4

Question 4

Simplify the expression:
k^5 x k^4

Answer 4

k^9

Question 5

Fully simplify the expression below:
4w^6 x 5w^2

Answer 5

20w^8

Question 6

What happens when we divide indices (powers) ?

Answer 6

Dividing indices (powers) means we must take away the powers

Question 7

What happens when we multiply indices (powers)?

Answer 7

Multiplying indices (powers) means we must add the powers

Question 8

Fully simplify: 4t^9 x 6t^-2
Give your answer without any negative indices

Answer 8

24t^7

Question 9

Fully simplify: 8f^4 x 7f^-20
Give your answer without any negative indices

Answer 9

56 x f^(4+-20)
= 56 x f^-16

= 56 x 1
——
f^16

= 56
——
f^16

Question 10

How can we rewrite a number to a negative index (power)?

Answer 10

x^-a = 1
——
x^a

Example:

1
——
f^16

Question 11

What would the indices do in this type of question: Simplify (x^a)^b
?

Answer 11

(x^a)^b in a question like this the powers always multiply. x^ a x b

Question 12

fully simplify (n^6 p^4)^3

Answer 12

n^18 p^12