Question

Evaluate:

A. 5 -1/6
B. 5 3/2
C. 5 5/2
D. 5 -5/6

Answer 1

@navk @VeritasVosLiberabit please help

Answer 2

The best thing to do first would be to make the equation simpler to solve:
\[\frac{ \sqrt[3]{5}\sqrt{5} }{ \sqrt[3]{5^{3}}\sqrt[3]{5^{2}} }\]

Answer 3

First convert each radical into an exponent; A square root is an exponent of 1/2 and a cube root is that of 1/3:\[\frac{5^{1/3}5^{1/2}}{{\left(5^5\right)}^{1/3}}\]

Answer 4

This then turns into \[\frac{ \sqrt{5} }{ \sqrt[3]{5^{2}}\sqrt[3]{5} }\]
You can make the process easier by changing the radicals into exponential form:
\[\frac{ 5^{1/2} }{5^{2/3}5^{1/3} }\]

Answer 5

this reduces down to \[\frac{ 5^{1/6} }{ 5^{2/3} }\]
then
\[\frac{ 1 }{ 5^{1/2} }\]

Answer 6

Simplify the denominator by multiplying the exponents 5 and 1/3:\[5^{5*1/3}=5^{5/3}\]Thus the expression becomes:\[\frac{5^{1/3}5^{1/2}}{{5}^{5/3}}\]Now add the exponents in the numerator and subtract those in the denominator\[5^{1/2+1/3-5/3}\]Add the fractions\[1/2+1/3-5/3=1/2-4/3=\frac{3-8}{6}=\frac{-5}{6}\]Hence the expression becomes\[5^{-5/6}\]

Answer 7

@navk has the right final answer here

Answer 8

oh my gosh sorry i didn't reply i got sidetracked

Answer 9

Thank you very much for your help!