Question

HELP! MEDAL :D

Answer 1

Evaluate

Answer 2

\[\large \frac{\sqrt[3]{5}\sqrt{5}}{\sqrt[3]{5^5}}\]

Answer 3

Lets see.. I would first rewrite the numerator as all fractions.

Answer 4

\[\large \frac{\sqrt[3]{5}\sqrt{5}}{\sqrt[3]{5^5}} = \frac{5^{1/3}\cdot 5^{1/2}}{5^{5/3}}\]

Answer 5

If you recall: \(\dfrac{5}{3} = \dfrac{1}{3} +\dfrac{4}{3}\)

Answer 6

So you can split the denominator as so: \(\large {5^{5/3} = 5^{1/3} \cdot 5^{4/3}}\)

Answer 7

http://postimg.org/image/g462vqd17/
This is the full question

Answer 8

Ok.

Answer 9

\[\large \frac{5^{1/3}\cdot 5^{1/2}}{5^{5/3}} = \frac{\color{red}{5^{1/3}} \cdot 5^{1/2}}{\color{red}{5^{1/3}} \cdot 5^{4/3}}\] the highlighted portion can cancel out, what are you left wih?

Answer 10

5 1/2 and 5 4/3

Answer 11

Good.

Answer 12

So now recall that when you have a number, \(n\) divided by the same number with a different power, and both of these numbers have powers \(x\) and \(y\), that the powers subtract?\[\large \frac{n^x}{n^y} = n^{x-y}\]

Answer 13

So let's say \(n=5\), can you use that subtraction method to find your rsult?

Answer 14

Losing connection... trying to reconnect. hmmm 5^x/ 5 ^y

Answer 15

B? @Jhannybean

Answer 16

no, not B. What is \(\dfrac{1}{2} - \dfrac{4}{3} =~?\)

Answer 17

@Jhannybean -0.8

Answer 18

and what is that in fraction form?

Answer 19

@AleshGames ?

Answer 20

8/10

Answer 21

-8/10

Answer 22

\[\frac{1}{2}-\frac{4}{3}\]make a common denominator. \[\frac{3}{6} - \frac{8}{6}\]\[\frac{3-8}{6} = -\frac{5}{6}\]