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Brian was asked to write x72 as a product of 2 powers with the same base in 4 different ways, using only positive exponents.
Which could be one of Brian's expressions?

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The equivalent expression to the value given using the laws of indices is  [tex] {x}^{4(18)} [/tex]

Evaluating the options given based on the laws of indices :

  • [tex] {x}^{8}. {x}^{9} = {x}^{8 + 9} = {x}^{17} [/tex]
  • [tex] {x}^{35}. {x}^{47} = {x}^{35 + 47} = {x}^{82} [/tex]
  • [tex] {x}^{4(18)} = {x}^{4 \times 18} = {x}^{72} [/tex]
  • [tex] {x}^{24}. {x}^{3} = {x}^{24 + 3} = {x}^{27} [/tex]

Therefore, the only expression which would give a correct way of representing [tex] {x}^{72} \: is \: {x}^{4(18)} [/tex]

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