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Indices, SM-Bank 058

  1. Write 216 as a product of its prime factors.  (2 marks)

  2. Hence find \(\sqrt[3]{216}\).  (2 marks)

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a.    \(2\times 2\times 2\times 3\times 3\times 3\)

b.    \(6\)

Show Worked Solution
a.    \(216\) \(=2\times 108\)
    \(=2\times 2\times 54\)
    \(=2\times 2\times 2\times 27\)
    \(=2\times 2\times 2\times 3\times 9\)
    \(=2\times 2\times 2\times 3\times 3\times 3\)

 

b.    \(\sqrt[3]{216}\) \(=\sqrt[3]{2\times 2\times 2\times 3\times 3\times 3}\)
    \(=\sqrt[3]{(2\times 3)\times (2\times 3)\times (2\times 3)}\)
    \(=\sqrt[3]{6\times 6\times 6}\)
    \(=6\)