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

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

jameslinimk

09.01.2022

${3}^{ \frac{3}{2} } = \sqrt[2]{27}$

Step-by-step explanation:

The given expresion is:

${3}^{ \frac{3}{2} }$

Recall the following property:

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

We compare

${3}^{ \frac{3}{2} }$

${a}^{ \frac{m}{n} }$

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

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

${3}^{ \frac{3}{2} } = \sqrt[2]{ {3}^{3} }$

We simplify this to get:

${3}^{ \frac{3}{2} } = \sqrt[2]{27}$

or simply:

${3}^{ \frac{3}{2} } = \sqrt{27}$

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