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Index notation
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EasyQuestion 1
[2 marks]Work out:
(a) 3⁴
(b) 10⁵
Solution for Question 1
MediumQuestion 2
[3 marks]Write each calculation as a single power:
(a) 2 × 2 × 2 × 2 × 2 × 2 × 2
(b) 5 × 5 × 5 × 5
(c) 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7 × 7
Solution for Question 2
HardQuestion 3
[3 marks]Without a calculator, work out the value of:
(a) 2⁶ + 3³
(b) 4³ ÷ 2⁴
Solution for Question 3
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Index notation is a shorthand for repeated multiplication. In the expression 2⁵, the base is 2 and the index (or power/exponent) is 5. It means 2 × 2 × 2 × 2 × 2 = 32.
Any number to the power of 1 equals itself: 5¹ = 5. Any number to the power of 0 equals 1: 5⁰ = 1 (this is a key rule to remember). The power tells you how many times to multiply the base by itself.
Index notation is essential for writing large numbers efficiently (like 10⁶ = 1,000,000) and for expressing prime factorisations neatly. It also connects to the laws of indices which you'll use extensively in algebra.
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