anonymous
  • anonymous
what is 2 4/3 equal to? the answer must be in square root form
Mathematics
jamiebookeater
  • jamiebookeater
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jdoe0001
  • jdoe0001
hmmm sounds what do they mean by "square root form"? that could mean anything
anonymous
  • anonymous
like the answer is an exponent and then there's a radical and then it has a base in the radical
anonymous
  • anonymous
\[2^\frac{ 4 }{3 }\]?

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anonymous
  • anonymous
|dw:1442875830908:dw|
anonymous
  • anonymous
yes
jdoe0001
  • jdoe0001
actually, got the colors backwards there =) \(\Large { a^{\frac{{\color{blue} n}}{{\color{red} m}}} \implies \sqrt[{\color{red} m}]{a^{\color{blue} n}} \qquad \qquad \sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}\qquad thus \\ \quad \\ 2^{\frac{{\color{blue}{ 4}}}{{\color{red}{ 3}}}}\implies ? }\)
anonymous
  • anonymous
so ^4 sqrt 2^3 ?
anonymous
  • anonymous
and then what's after that
jdoe0001
  • jdoe0001
hmmm the numerator is the exponent the denominator is the root
jdoe0001
  • jdoe0001
\(\large { \sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}\qquad thus \\ \quad \\ 2^{\frac{{\color{blue}{ 4}}}{{\color{red}{ 3}}}}\implies \sqrt[{\color{red}{ 3}}]{2^{{\color{blue}{ 4}}}}\implies \sqrt[3]{2\cdot 2\cdot 2\cdot 2\cdot 2}\implies \sqrt[3]{2^3\cdot 2^1}\implies 2\sqrt[3]{2} }\)
jdoe0001
  • jdoe0001
hmm actuallly, I have an extra 2 there =) \(\large { \sqrt[{\color{red} m}]{a^{\color{blue} n}}\implies a^{\frac{{\color{blue} n}}{{\color{red} m}}}\qquad thus \\ \quad \\ 2^{\frac{{\color{blue}{ 4}}}{{\color{red}{ 3}}}}\implies \sqrt[{\color{red}{ 3}}]{2^{{\color{blue}{ 4}}}}\implies \sqrt[3]{2\cdot 2\cdot 2\cdot 2}\implies \sqrt[3]{2^3\cdot 2^1}\implies 2\sqrt[3]{2} }\)
anonymous
  • anonymous
oh so it'd be 3 sqrt 16

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