Index laws: multiplying and dividing

The Maths Habit

  1. Write 6 × 6 × 6 × 6 in index form.

    64
  2. Work out 27.

    128
  3. Which is bigger: 34 or 43?

    34 (81 is bigger than 64)

One grain of rice on the first square of a chessboard, two on the next, then four, doubling each time. How many grains are on the last square?

About 9 million million million

Write out in full

43 4 × 4 × 4

Base
The number that is being multiplied.
Index
The small number that says how many times to multiply. Also called a power.

23 × 22

2×2×2×2×2

Write 24 × 25 as a single power of 2.

2×2×2×224×2×2×2×2×225×
Write each power out in full.
24 × 25 = 29

Write 53 × 56 as a single power of 5.

5×5×553×5×5×5×5×5×556×
Write each power out in full.
53 × 56 = 59

Write 24 × 25 as a single power of 2.

2×2×2×224×2×2×2×2×225×
Write each power out in full.
24 × 25 = 29

Write 82 × 87 as a single power of 8.

8×882×8×8×8×8×8×8×887×
Write each power out in full.
82 × 87 = 89

Write 47 ÷ 43 as a single power of 4.

4×4×4×4×4×4×4×4×4×4×××××
Write each power out in full.
47 ÷ 43 = 44

Write 65 ÷ 62 as a single power of 6.

6×6×6×6×6×××6×6××××××
Write each power out in full.
65 ÷ 62 = 63

Write 47 ÷ 43 as a single power of 4.

4×4×4×4×4×4×4×4×4×4×××××
Write each power out in full.
47 ÷ 43 = 44

Write 28 ÷ 25 as a single power of 2.

2×2×2×2×2×2×2×22×2×2×2×2×××
Write each power out in full.
28 ÷ 25 = 23

Write 24 × 25 as a single power of 2.

2×2×2×224×2×2×2×2×225×
Write each power out in full.
24 × 25 = 29

Write 35 × 32 as a single power of 3.

3×3×3×3×335×3×332×××
Write each power out in full.
35 × 32 = 37

Write 47 ÷ 43 as a single power of 4.

4×4×4×4×4×4×4×4×4×4×××××
Write each power out in full.
47 ÷ 43 = 44

Write 75 ÷ 72 as a single power of 7.

7×7×7×7×7×××7×7××××××
Write each power out in full.
75 ÷ 72 = 73

Write 47 ÷ 43 as a single power of 4.

4×4×4×4×4×4×4×4×4×4×××××
Write each power out in full.
47 ÷ 43 = 44

Write 68 ÷ 67 as a single power of 6.

6×6×6×6×6×6×6×66×6×6×6×6×6×6×
Write each power out in full.
68 ÷ 67 = 61

Index laws: multiplying and dividing worksheet, page 1

Index laws: multiplying and dividing worksheet, page 2

Answer sheet

  1. Sam says 23 × 32 = 65. What has he done wrong?

    The bases are different
  2. Write 54 ÷ 54 as a single power of 5. What is it as an ordinary number?

    50, which is 1

  1. Write 64 × 65 as a single power.

    69
  2. Write 98 ÷ 92 as a single power.

    96
  3. Ben says 56 ÷ 53 = 52. What has he done wrong? Write the right answer.

    53
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