What is 3 3/2 equal to? ∛9 ²√9 ³√27 ²√27

Question

asked Nov 11, 2020 29.9k views

1 Answer

Peonicles · Answer 1 · 2020-11-17T21:21:59+0000

Answer:

${3}^{ (3)/(2) } = \sqrt[2]{27}$

Explanation:

The given expresion is:

${3}^{ (3)/(2) }$

Recall the following property:

${a}^{ (m)/(n) } = \sqrt[n]{ {a}^(m) }$

We compare

${3}^{ (3)/(2) }$

to

${a}^{ (m)/(n) }$

We obtain a=3, m=3 and n=2

When we plug these values into the above property, we get:

${3}^{ (3)/(2) } = \sqrt[2]{ {3}^(3) }$

We simplify this to get:

${3}^{ (3)/(2) } = \sqrt[2]{27}$

or simply:

${3}^{ (3)/(2) } = √(27)$