Question

Simplify 4th root of 400/ 4th root of 5

Answer 1

Please explain ur answer cause I keep gettin it wrong

Answer 2

\[\frac{\sqrt[4]{100}}{\sqrt[4]{5}}\]?

Answer 3

@kimmii23 ???

Answer 4

yess
but its 400 instead of 100

Answer 5

\[\sqrt[a]{b}=b^{\frac{1}{a}}\\and\\\frac{a^b}{c^b}=(\frac{a}{c})^b\]
so
\[\frac{\sqrt[4]{400}}{\sqrt[4]{5}}=(\frac{400}{5})^{\frac{1}{4}}=(80)^{\frac{1}{4}}=\sqrt[4]{80}=\sqrt[4]{16*5}=\sqrt[4]{16}\sqrt[4]{5}=2\sqrt[4]{5}\]

Answer 6

\[\sqrt[a]{b*c}=\sqrt[4]{b}*\sqrt[a]{c}\]

Answer 7

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
\[ 2\sqrt[4]{5}\]

Answer 8

OHHHH! I got stuck at the 80 that was my issue..didnt break that down thanks