remember rules of exponents
[tex] x^{ \frac{z}{y} } = \sqrt[y]{x^{z}} [/tex]
combine because another rule is
√x times √y=√(xy) so
if we can make the denomenator of all fractions the same, then we can have a common root so
2 3 and 4
common number is 12 so
convert bottom number to 12 so
1/2=6/12
2/3=8/12
3/4=9/12
so the equation is
[tex] 3^{ \frac{6}{12} } [/tex] times [tex] a^{ \frac{8}{12} } [/tex] times [tex] b^{ \frac{9}{12} } [/tex]
this equals
[tex] \sqrt[12]{3^{6}} [/tex] times [tex] \sqrt[12]{a^{8}} [/tex] times [tex] \sqrt[12]{b^{9}} [/tex]
since we can combine we get
[tex] \sqrt[12]{ 3^{6} a^{8} b^{9} } [/tex]
