Fractional and negative indices

The Maths Habit

What comes next?

24 = 1623 = 822 = 421 = 220 = 12−1 = 122−2 = 14

Work out

  1. √36

    6

  2. ∛8

    2

  3. √144

    12

  4. ∛125

    5

The bottom of the fraction is the root

The top of the fraction is the power

A negative means 1 over

Work out

912 3

Work out

813 2

Work out 1632.

the bottom is the root4the top is the power64
Answer64

Work out 2743.

the bottom is the root3the top is the power81
Answer81

Work out 1632.

the bottom is the root4the top is the power64
Answer64

Work out 10032.

the bottom is the root10the top is the power1000
Answer1000

Work out

3−1 13

Work out 5−2.

the power25a negative means 1 over125
Answer125

Work out 10−3.

the power1000a negative means 1 over11000
Answer11000

Work out 5−2.

the power25a negative means 1 over125
Answer125

Work out 3−4.

the power81a negative means 1 over181
Answer181

Work out 1632.

the bottom is the root4the top is the power64
Answer64

Work out 452.

the bottom is the root2the top is the power32
Answer32

Work out 5−2.

the power25a negative means 1 over125
Answer125

Work out 7−2.

the power49a negative means 1 over149
Answer149

Work out 1632.

the bottom is the root4the top is the power64
Answer64

Work out 100023.

the bottom is the root10the top is the power100
Answer100

Fractional and negative indices worksheet, page 1

Answer sheet

  1. Write 18 as a power of 2.

    2−3

  2. Find n if 9n = 27.

    32

  3. Work out 64−23.

    116

  1. Work out 12523

    25

  2. Work out 2−5

    132

  3. Work out 16−34

    18
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