Question

Which is equivalent to7^(3/2) over 7^(1/2)?

Answer 1

Given the expression below:

$\large{ \frac{ {7}^{ \frac{3}{2} } }{ {7}^{ \frac{1}{2} } } }$

Use the following property:

$\large \boxed{ {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } }$

Therefore:

$\large{ \frac{ {7}^{ \frac{3}{2} } }{ {7}^{ \frac{1}{2} } } = \frac{ \sqrt{ {7}^{3} } }{ \sqrt{7} } } \\ \large{ \frac{ \sqrt{ {7}^{3} } }{ \sqrt{7} } = \frac{ \sqrt{7 \times 7 \times 7} }{ \sqrt{7} } \longrightarrow \frac{7 \sqrt{7} }{ \sqrt{7} } } \\ \large{ \frac{7 \cancel{ \sqrt{7} }}{ \cancel{ \sqrt{7} }} = 7}$

Note that a¹ = a. Therefore, 7¹ = 7.

Answer

• 7¹ or 7.

Answer 2

The answer is c! you just subtract: 3/2-1/2, which is 1.