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
$\frac{x^m}{x^n}=x^{m-n}$
and
(ab)/c=(a/c)(b/c)
and
$\sqrt[n]{x^m} =x^ \frac{m}{n}$
and
$(x^m)^n=x^{mn}$
and
x^-m=1/(x^m)


so
first convert 8 to 2³

$\frac{ \sqrt[5]{2^3} \sqrt[2]{2^3} }{ \sqrt[3]{(2^3)^5} }$=
$\frac{(2^ \frac{3}{5})(2^ \frac{3}{2}) }{2^ \frac{15}{3} }$=
we can simplify $2^ \frac{15}{3} $ to $2^5 $
$\frac{(2^ \frac{3}{5})(2^ \frac{3}{2}) }{2^5}$=
$( \frac{2^ \frac{3}{5}}{2^5} )( \frac{2^ \frac{3}{2}}{2^5} )$
(3/5)-5=3/5-25/5=-22/5
3/2-5=3/2-10/2=-7/2
$(2^ \frac{-22}{5})(2^ \frac{-7}{2})$
-22/5+(-7/2)=
-44/10-35/10=
-79/10=-7 and 9/10
$2^{-7&\frac{9}{10}=\frac{1}{7 \sqrt[10]{2^9} }$

sorry for complex stuff