Algebra potensregning

Algebra potensregning

Skriv så enkelt som mulig

(2ab1)3(a2b2)14a2b3\frac{\left( 2ab^{-1} \right)^3 \cdot \left( a^2b^{-2} \right)^{-1} }{4a^2b^{-3}}
Fasit

2ba\frac{2b}{a}

Løsningsforslag
(2ab1)3(a2b2)14a2b3=23a3b13a2(1)b(2)(1)a2b34=84a(322)b(3+2+3)=2b2a\frac{\left( 2ab^{-1} \right)^3 \cdot \left( a^2b^{-2} \right)^{-1} }{4a^2b^{-3}} = \frac{2^3a^3b^{-1\cdot3}a^{2\cdot(-1)}b^{(-2)\cdot(-1)}a^{-2}b^{3}}{4}=\frac{8}{4}\cdot a^{(3-2-2)}\cdot b^{(-3+2+3)}=\underline{\underline{\frac{2b^2}{a}}}