square root cube root integer evaluate index laws

square root cube root integer evaluate index laws zero index verify evaluate index notation Indices Vocabulary: index indices base power exponent prime composite divisibility factors square

Indices Main points covered in this unit: • • Describe numbers using index form Evaluate numbers expressed using powers Use divisibility tests correctly Write numbers using prime factors Find the highest common factor of numbers Use order of operations Use index laws to simplify expressions

Indices Why use indices? According to legend, chess was invented by Grand Vizier Sissa Ben Dahir, and given to King Shirham of India. The king offered him a reward, and he requested the following: "Just one grain of wheat on the first square of the chessboard. Then put two on the second square, four on the next, then eight, and continue, doubling the number of grains on each successive square, until every square on the chessboard is reached. "

Indices Writing Indices

Put the terms in the correct columns: Indices

Index Laws – short cuts! Indices

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What’s the difference between a factor and a multiple? Indices

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Prime Factor Trees Indices The highest common factor (HCF) of two numbers is the biggest number which divides evenly into both of them. Two ways to do this are using lists, and using factor trees. e. g. Find the HCF of 36 and 64: 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 64: 1, 2, 4, 8, 16, 32, 64 So HCF of 36 and 64 is 4 Look for the common factors in the bottom line and multiply them all together – in this case ‘ 2 x 2’ which also gives 4.

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Indices Create a factor tree for each number, then use them to find the Highest Common Factor (HCF) and Lowest Common Multiple (LCM) for each pair. a) 20 36 b) 60 16 c) 15 35 d) 28 36

Indices Divisibility tests: How do we know if a number has factors?

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Squares and Cubes Indices

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Challenge Questions! 1 2 3 4 Indices

Challenge Questions! Indices