Fractional Indices

Starter Simplify the following… a) 4-2 b) 2-4 c) 3-8 d) 5-1 e) 40 f) 4-2 x 4-3 Find the value of… a) 4-3 b) 2-5 c) 3-2 d) 5-3 e) 4-1 f) 6-2 x 63 1/42 1/24 1/38 1/5 1 1/45 1/64 1/32 1/9 1/125 1/4 6

Fractional Indices We have seen how to deal with Negative Indices We saw that a Negative power turns the term into a Fraction Today we will see how to work out what a Fractional Power means

Fractional Indices 4 x 4 = 4 2 x 2 = 4 4 = 2 Remember when multiplying, we add the powers… 1 2 1 2 1 4 x 4 = 4 These numbers must be the same 2 x 2 = 4 1 2 4 = 2 Therefore

Fractional Indices 9 x 9 = 9 3 x 3 = 9 9 = 3 Remember when multiplying, we add the powers… 1 2 1 2 1 9 x 9 = 9 These numbers must be the same 3 x 3 = 9 1 2 9 = 3 Therefore

These numbers must be the same Fractional Indices 1 2 1 2 1 25 x 25 = 25 These numbers must be the same 5 x 5 = 25 1 2 25 = 5 Therefore

You can leave them as surds Fractional Indices 1 2 4 = 2 ‘If something is raised to the power 1/2 , you work out the square root’ 1 2 9 = 3 1 2 25 = 5 1 2 You can leave them as surds 2 = √2

These numbers must be the same Fractional Indices 1 3 1 3 1 3 1 8 x 8 x 8 = 8 These numbers must be the same 2 x 2 x 2 = 8 1 3 8 = 2 Therefore

These numbers must be the same Fractional Indices 1 3 1 3 1 3 1 1000 x 1000 x 1000 = 1000 These numbers must be the same 10 x 10 x 10 = 1000 1 3 1000 = 10 Therefore

Fractional Indices 8 = 2 1000 = 10 27 = 3 5 = 1 3 8 = 2 ‘If something is raised to the power 1/3, you work out the cube root’ 1 3 1000 = 10 1 3 27 = 3 1 3 You can leave them as surds 5 = 3√5

Fractional Indices 1 2 x = √x 1 3 x = 3√x 1 4 x = 4√x 1 m x = m√x

Fractional Indices 8 x 8 = 8 2 x 2 = 4 8 = 4 1 3 1 3 2 3 Work out the cube roots 2 x 2 = 4 2 3 8 = 4 Therefore

Fractional Indices 27 x 27 = 27 3 x 3 = 9 27 = 9 1 3 1 3 2 3 Work out the cube roots 3 x 3 = 9 2 3 27 = 9 Therefore

Fractional Indices 10 x 10 = 10 x = (3√10)2 (3√10)2 10 = 3√10 3√10 1 3 2 3 10 x 10 = 10 Write as a surd 3√10 x 3√10 = (3√10)2 2 3 (3√10)2 10 = Therefore

Fractional Indices 7 x 7 x 7 = 7 x x = (5√7)3 (5√7)3 7 = 5√7 5√7 5√7 1 5 1 5 1 5 3 5 7 x 7 x 7 = 7 Write as surds x x 5√7 5√7 5√7 = (5√7)3 3 5 (5√7)3 7 = Therefore

Fractional Indices 10 = (3√10)2 7 = (5√7)3 2 = (7√2)4 x = (m√x)n 2 3 3 5 7 = (5√7)3 4 7 2 = (7√2)4 n m x = (m√x)n

Plenary = (3√8)4 = (2)4 16

Plenary 1/100 x 8 0.01 x 8 0.08 23 (3√x)2 = x (3√8)2 = 4

Summary We have learnt how to deal with Fractional Indices We have also seen how to rewrite them when both the numerator and denominator are not equal to 1