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:
Louis
Explanation:
To determine the solution to this problem, we apply the addition law of indices.
[tex]\text{Addition Law of Indices: }a^x\times a^y=a^{x+y}[/tex]Therefore, if we have:
[tex]\begin{gathered} 4^2\text{ }\times4^5 \\ \text{Applying the addition law of indices, we have:} \\ 4^2\text{ }\times4^5=4^{2+5} \\ =4^7 \end{gathered}[/tex]Therefore, Louis has the correct answer.