Penjelasan
Sifat-sifat Eksponensial
- [tex]a^n = \frac{1}{a^{-n}}[/tex]
- [tex]a^n ~.~b^n= (ab)^n[/tex]
- [tex]a^n~.~a^m =a^{n+m}[/tex]
- [tex]\frac{a^n}{a^m} = a^{n-m}[/tex]
Penyelesaian
Bagian A.
[tex]\left(\frac{8}{27} \right)^{\frac{1}{3} }[/tex]
[tex]= \left(\frac{2^3}{3^3} \right)^{\frac{1}{3} }[/tex]
[tex]= \left(\left(\frac{2}{3} \right)^3\right)^{\frac{1}{3} }[/tex]
[tex]= \left(\frac{2}{3} \right)^{\frac{3}{3} }[/tex]
[tex]= \boxed{\frac{2}{3} }[/tex]
Bagian B.
[tex]16^{-\frac{1}{2} } ~. ~(8)^{\frac{5}{3} }[/tex]
[tex]= (4^2)^{-\frac{1}{2} } ~. ~(2^3)^{\frac{5}{3} }[/tex]
[tex]= 4^{-\frac{2}{2} } ~. ~2^{\frac{5~.~3}{3} }[/tex]
[tex]= 4^{-1 } ~. ~2^5[/tex]
[tex]= \frac{1}{4} ~.~ 32[/tex]
[tex]= \boxed{8}[/tex]
Bagian C.
[tex]\frac{\sqrt{9^3}~.~8^{\frac{2}{3} } }{36^{0,5}}[/tex]
[tex]=\frac{\sqrt{3^{2.3}}~.~(2^3)^{\frac{2}{3} } }{^{(6^2)^{\frac{1}{2} }}}[/tex]
[tex]= \frac{3^3~.~2^2}{6}[/tex]
[tex]= \frac{3^3~.~2^2}{3~.~2}[/tex]
[tex]= 3^2~.~2[/tex]
[tex]= \boxed{18}[/tex]
Bagian D.
[tex]\frac{12^{\frac{7}{12}}~.~2^{\frac{5}{6}} }{6^{\frac{2}{3}}~.~2^{\frac{1}{4} }}[/tex]
[tex]=\frac{(6.2)^{\frac{7}{12}}~.~2^{\frac{5}{6} - \frac{1}{4} } }{6^{\frac{2}{3}}}[/tex]
[tex]=\frac{6^{\frac{7}{12}}~.~2^{\frac{7}{12}}~.~2^{\frac{10-3}{12} } }{6^{\frac{2}{3}}}[/tex]
[tex]=6^{\frac{7}{12}-\frac{2}{3} }~.~2^{\frac{7}{12}+\frac{7}{12}}[/tex]
[tex]=6^{\frac{7 - 8}{12}}~.~2^{\frac{14}{12}}[/tex]
[tex]=6^{-\frac{1}{12}}~.~2^{\frac{14}{12}}[/tex]
[tex]=(3.2)^{-\frac{1}{12}}~.~2^{\frac{14}{12}}[/tex]
[tex]=3^{-\frac{1}{12}}~.~2^{-\frac{1}{12}}~.~2^{\frac{14}{12}}[/tex]
[tex]= \frac{2^{\frac{13}{12}} }{3^{\frac{1}{12}} }[/tex]
[tex]= \boxed{\left(\frac{2^{13} }{3}\right)^{\frac{1}{12} }}~~atau~~\boxed{\sqrt[12]{\frac{2^{13}}{3} } }[/tex]
