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

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1. anonymous

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. anonymous

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. anonymous

hmmm the numerator is the exponent the denominator is the root

10. anonymous

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

11. anonymous

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

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