Indices 2

Question 1

Negative powers

How do you work out a⁻ⁿ where a is 8 and n is 2?

Answer 1

a⁻ⁿ = 1/aⁿ

1/8²

1/64

Question 2

Reciprocals

What is a⁻ⁿ when a is (5/9) and n is -1?

Answer 2

a⁻¹ = 1/a

9/5

Question 3

Powers of fractions

What is (a/b)ⁿ when a=3, b=10 and n=2?

Answer 3

(a/b)ⁿ = aⁿ /bⁿ

3²/10² = 9/100

Question 4

Combining rules

(a/b)⁻ⁿ

a = 2
b = 3
n = 3

Answer 4

(a/b)⁻ⁿ = (b/a)ⁿ = bⁿ/aⁿ

(3/2)³ = 3³/2³ = 27/8

Question 5

Fractional powers

a¹/² when a=49

a¹/³ when a=27

a¹/⁴ when a=16

Answer 5

a¹/² = √a
a¹/³ = ³√a
a¹/⁴ = ⁴√a

49¹/² = √49 = 7
27¹/³ = 3
16¹/⁴ = 2

Question 6

Complicated indices

aⁿ¹/ⁿ²

a = 27
ⁿ¹ = -2
ⁿ² = 3

Answer 6

aⁿ¹/ⁿ² = (a¹/ⁿ²)ⁿ¹

27⁻²/³ = (27¹/³)⁻² = (³√27)⁻²

= 3⁻² = 1/3² = 1/9