anonymous
  • anonymous
Simplify 4th root of 400/ 4th root of 5
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Please explain ur answer cause I keep gettin it wrong
zzr0ck3r
  • zzr0ck3r
\[\frac{\sqrt[4]{100}}{\sqrt[4]{5}}\]?
zzr0ck3r
  • zzr0ck3r
@kimmii23 ???

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anonymous
  • anonymous
yess but its 400 instead of 100
zzr0ck3r
  • zzr0ck3r
\[\sqrt[a]{b}=b^{\frac{1}{a}}\\and\\\frac{a^b}{c^b}=(\frac{a}{c})^b\] so \[\frac{\sqrt[4]{400}}{\sqrt[4]{5}}=(\frac{400}{5})^{\frac{1}{4}}=(80)^{\frac{1}{4}}=\sqrt[4]{80}=\sqrt[4]{16*5}=\sqrt[4]{16}\sqrt[4]{5}=2\sqrt[4]{5}\]
zzr0ck3r
  • zzr0ck3r
\[\sqrt[a]{b*c}=\sqrt[4]{b}*\sqrt[a]{c}\]
phi
  • phi
ssrock showed how you can simplify the problem to 4th root of 80 to find the 4th root of 80, factor 80 into its prime factors: 2*40 = 2* 2*20= 2*2*2*10= 2*2*2*2*5 and look for "groups of 4" (because you are doing 4th root) there is only one group of four 2's. you can take out the 4 twos, and replace them with 1 two on the outside. the 5 stays inside you get \[ 2\sqrt[4]{5}\]
anonymous
  • anonymous
OHHHH! I got stuck at the 80 that was my issue..didnt break that down thanks

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