Question

5 √8 √8/3√8^5 Can someone explain this please??  Am I doing this right.  =8 1/5 8 1/2 divided by (8 1/3)^5  then I get stuck

Answer 1

remember

`(x^m)/(x^n)=x^(m-n)`
and
(ab)/c=(a/c)(b/c)
and

`\sqrt[n]{x^m} =x^ (m)/(n)`
and

`(x^m)^n=x^(mn)`
and
x^-m=1/(x^m)


so
first convert 8 to 2³


`\frac{ \sqrt[5]{2^3} \sqrt[2]{2^3} }{ \sqrt[3]{(2^3)^5} }`=

`((2^ (3)/(5))(2^ (3)/(2)) )/(2^ (15)/(3) )`=
we can simplify
`2^ (15)/(3)` to
`2^5`

`((2^ (3)/(5))(2^ (3)/(2)) )/(2^5)`=

`( (2^ (3)/(5))/(2^5) )( (2^ (3)/(2))/(2^5) )`
(3/5)-5=3/5-25/5=-22/5
3/2-5=3/2-10/2=-7/2

`(2^ (-22)/(5))(2^ (-7)/(2))`
-22/5+(-7/2)=
-44/10-35/10=
-79/10=-7 and 9/10

`2^{-7&(9)/(10)=\frac{1}{7 \sqrt[10]{2^9} }`

sorry for complex stuff