Question

Brian was asked to write x72 as a product of 2 powers with the same base in 4 different ways, using only positive exponents.

Answer 1

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

Evaluating the options given based on the laws of indices :

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

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

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