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.

Harry Louis and Niall are working with exponents Harry claims 42 X45410 Louis claims 42X 4547 Niall claims 42X45167 Which student has the correct answer Explain class=

Respuesta :

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.