## anonymous one year ago what is 2 4/3 equal to? the answer must be in square root form

1. jdoe0001

hmmm sounds what do they mean by "square root form"? that could mean anything

2. anonymous

like the answer is an exponent and then there's a radical and then it has a base in the radical

3. anonymous

$2^\frac{ 4 }{3 }$?

4. anonymous

|dw:1442875830908:dw|

5. anonymous

yes

6. jdoe0001

actually, got the colors backwards there =) $$\Large { a^{\frac{{\color{blue} n}}{{\color{red} m}}} \implies \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad \sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}\qquad thus \\ \quad \\ 2^{\frac{{\color{blue}{ 4}}}{{\color{red}{ 3}}}}\implies ? }$$

7. anonymous

so ^4 sqrt 2^3 ?

8. anonymous

and then what's after that

9. jdoe0001

hmmm the numerator is the exponent the denominator is the root

10. jdoe0001

$$\large { \sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}\qquad thus \\ \quad \\ 2^{\frac{{\color{blue}{ 4}}}{{\color{red}{ 3}}}}\implies \sqrt[{\color{red}{ 3}}]{2^{{\color{blue}{ 4}}}}\implies \sqrt[3]{2\cdot 2\cdot 2\cdot 2\cdot 2}\implies \sqrt[3]{2^3\cdot 2^1}\implies 2\sqrt[3]{2} }$$

11. jdoe0001

hmm actuallly, I have an extra 2 there =) $$\large { \sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}\qquad thus \\ \quad \\ 2^{\frac{{\color{blue}{ 4}}}{{\color{red}{ 3}}}}\implies \sqrt[{\color{red}{ 3}}]{2^{{\color{blue}{ 4}}}}\implies \sqrt[3]{2\cdot 2\cdot 2\cdot 2}\implies \sqrt[3]{2^3\cdot 2^1}\implies 2\sqrt[3]{2} }$$

12. anonymous

oh so it'd be 3 sqrt 16