Question

What is 3 to the power of 3 over 2 equal to?

Answer 1

well... what's \(\bf 3^3 \quad ?\)

Answer 2

it is 27

Answer 3

3x3x3 = 27

Answer 4

well, then \(\bf \cfrac{3^3}{2}\implies \cfrac{27}{2}\implies 13\frac{1}{2}\implies 13.5\)

Answer 5

no i mean like 3^3/2

Answer 6

\(\bf {\color{blue}{ \cfrac{3^3}{2}}}\implies \cfrac{27}{2}\implies 13\frac{1}{2}\implies 13.5\)

Answer 7

thats the same thing

Answer 8

3^3/2

Answer 9

that is my question

Answer 10

ohhh I see Ithink you mean \(\huge 3^{\frac{3}{2}}\quad ?\)

Answer 11

yes perfect

Answer 12

\(\large \bf{ 3^{\frac{3}{2}}
\\ \quad \\
a^{\frac{{\color{blue} n}}{{\color{red} m}}} = \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad thus
\\ \quad \\
3^{\frac{3}{2}}\implies \sqrt[{\color{red}{ 2}}]{3^{\color{blue}{ 3}}} }\implies \sqrt{3\cdot 3\cdot 3}\implies \sqrt{3\cdot 3}\cdot \sqrt{3}\implies \sqrt{3^2}\cdot \sqrt{3}\)

what would that simplify to?

Answer 13

id really know...

Answer 14

i am bad at this concept

Answer 15

well, just keep in mind that, any FACTOR inside the radical, that matches the root, goes "over the root" fence per se =)
so \(\large \bf \sqrt[{\color{blue}{ n}}]{x^{\color{blue}{ n}}} \iff x\)

so.. which one do you think we could take out?

Answer 16

i honestly dont know but if u want options,
here:


cube root of 9

square root of 9

cube root of 27

square root of 27

Answer 17

i think it is the last one... what do u say?

Answer 18

well \(\bf 3^{\frac{3}{2}}\implies \sqrt[{\color{red}{ 2}}]{3^{\color{blue}{ 3}}}\implies \sqrt{3\cdot 3\cdot 3}\implies \sqrt{27}\)

Answer 19

so im right?

Answer 20

yeap

Answer 21

3*3*3 = 27