DJJo
  • DJJo
Will give medal! How do I simplify the square root of the fourth root of 8 in exponential form?
Algebra
schrodinger
  • schrodinger
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DJJo
  • DJJo
anonymous
  • anonymous
\[\sqrt{\sqrt[4]{8}}=\sqrt{8^{\frac{ 1 }{ 4}}}=(8^{\frac{ 1 }{ 4 }})^{\frac{ 1 }{ 2 }}=8^{\frac{ 1 }{ 8}}=(2^{3})^{\frac{ 1 }{ 8 }}=2^{\frac{ 3 }{ 8 }}\]
DJJo
  • DJJo
But I'm confused on how you got that @peachpi

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anonymous
  • anonymous
how is it confusing? things to power are multiplied with each other
anonymous
  • anonymous
square root is the same as the exponent ½ fourth root is exponent ¼
DJJo
  • DJJo
oh ok thank you @peachpi
DJJo
  • DJJo
@peachpi Would you mind if I ask you another question?
anonymous
  • anonymous
ok
DJJo
  • DJJo
How would I simply this expression in exponential form?
anonymous
  • anonymous
ok. this is the same type of problem. How would you write the numerator with an exponent?
DJJo
  • DJJo
3 and 1/2
anonymous
  • anonymous
exponents with bases being divided are subtracted eg. 3^(1/2) / 3^(1/4) = 3^ ((1/2) - (1/4))
anonymous
  • anonymous
Yeah. Then √3 is also a part of the denominator so you can do this |dw:1434904015717:dw|
DJJo
  • DJJo
So would the denominator be 3 and 1/8?
anonymous
  • anonymous
no... 3 and 1/4
anonymous
  • anonymous
It would be 3^(1/4) because 1/2 * 1/2 = 1/4
anonymous
  • anonymous
|dw:1434904157793:dw|
anonymous
  • anonymous
Now since the base is 3 on top and bottom you can subtract the exponents
anonymous
  • anonymous
1/4 since as I have explained before... exponents, with bases same being multiplied, are added
anonymous
  • anonymous
|dw:1434904205322:dw|
DJJo
  • DJJo
So 3 and 1/4 would be the answer right?
anonymous
  • anonymous
3 TO THE 1/4
DJJo
  • DJJo
Yeah, that's what meant Thank you sooooo much @peachpi
anonymous
  • anonymous
you're welcome

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