Given the expression below:
[tex] \large{ \frac{ {7}^{ \frac{3}{2} } }{ {7}^{ \frac{1}{2} } } }[/tex]
Use the following property:
[tex] \large \boxed{ {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } }[/tex]
Therefore:
[tex] \large{ \frac{ {7}^{ \frac{3}{2} } }{ {7}^{ \frac{1}{2} } } = \frac{ \sqrt{ {7}^{3} } }{ \sqrt{7} } } \\ \large{ \frac{ \sqrt{ {7}^{3} } }{ \sqrt{7} } = \frac{ \sqrt{7 \times 7 \times 7} }{ \sqrt{7} } \longrightarrow \frac{7 \sqrt{7} }{ \sqrt{7} } } \\ \large{ \frac{7 \cancel{ \sqrt{7} }}{ \cancel{ \sqrt{7} }} = 7}[/tex]
Note that a¹ = a. Therefore, 7¹ = 7.
Answer
