Question

Harry, Louis, and Niall are working with exponents. Harry claims 4^{2} X4^{5}=4^{10}. Louis claims 4^{2}X 4^{5}=4^{7}. Niall claims 4^{2}X4^{5}=16^{7}. Which student has the correct answer? Explain why.

Answer 1

Louis

Step-by-step explanation:

To determine the solution to this problem, we apply the addition law of indices.

`\text{Addition Law of Indices: }a^x* a^y=a^(x+y)`

Therefore, if we have:

`\begin{gathered} 4^2\text{ }*4^5 \\ \text{Applying the addition law of indices, we have:} \\ 4^2\text{ }*4^5=4^(2+5) \\ =4^7 \end{gathered}`

Therefore, Louis has the correct answer.