N4 Integers and Powers

Question 1

What is x to the power of -n?

Answer 1

1 / x to the power of n

Question 2

What is x to the power of 1/n?

Answer 2

The nth root of x

Question 3

What is x to the power of m times x to the power of n?

Answer 3

x to the power of n+m

Question 4

What is x to the power of m divided by x to the power of n?

Answer 4

x to the power of m-n

Question 5

What is x to the power of 0?

Answer 5

1

Question 6

What is (x to the power of m) to the power of n?

Answer 6

x to the power of mn

Question 7

What is x to the power of m / n?

Answer 7

The nth root of x to the power of m

Question 8

What is x to the power of -m / n?

Answer 8

1 / the nth root of x to the power of m

Question 9

What is x to power of a half times x to the power of a half?

Answer 9

x

Question 10

What are the first ten prime numbers?

Answer 10

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Question 11

Write 30 as a product of its prime factors.

Answer 11

30 / 2
15 / 3
5 / 5
1

So 30 = 2 x 3 x 5

Question 12

How would you find the highest common factor of 54 and 84?

Answer 12

Write each as a product of their prime factors:

54 / 2 84 / 2
27 / 3 42 / 2
9 / 3 21 / 3
3 / 3 7 / 7
1 1

54 = 2 x 3 x 3 x 3 84 = 2 x 2 x 3 x 7

Make diagrams:

Factors of 54 Both Factors of 84

3 3 3 2 2 7

So HCF = product of similar factors
So HCF = 3 x 2 = 6.

Question 13

How would you find the LCM of 60 and 280?

Answer 13

Find the products of their prime factors for each.

Make diagram of factors for 60, 280 and both.

Multiply ALL numbers in diagram = LCM.