Unit 3 Section 5 : Fractional Indices

Indices that are fractions are used to represent square roots, cube roots and other roots of numbers.

a = for example, 9 = 3
a = for example, 8 = 2
a = for example, 625 = 5
a =

Example 1

Calculate:

(a)
81
(b)
1000
(c)
4

Exercises

Question 1
Calculate:
(a)
49
(b)
64
(c)
16
(d)
81
(e)
100
(f)
25
(g)
9
(h)
36
(i)
144
Question 2
Calculate:
(a)
8
(b)
8
(c)
125
(d)
64
(e)
216
(f)
1 000 000
Question 3
Calculate:
(a)
32
(b)
64
(c)
10 000
(d)
81
(e)
625
(f)
100 000
Question 4
Calculate:
(a)
()
(b)
()
(c)
()
(d)
()
Question 5
Is each of the following statements true or false:
(a)
16 = 8
(b)
16 = 2
(c)
81 = 9
(d)
() = 10
Question 6
Simplify:
(a)
(x9)
x
(b)
(a10)
a
(c) a
(d) a
Question 7
Simplify:
(a) x
(b) x
(c) a
(d) a
Question 8
Calculate:
(a)
4 + 4
(b)
( 90 + 9)
(c)
( 256)
(d)
(9 90)