Răspuns:
Explicație pas cu pas:
[tex]\frac{(a^{\frac{2}{5} })^{20} * (a^{-1}*b^{1,(6)} )^{\frac{3}{2} } } {a^{2,5} * (b^{22})^{\frac{1}{8} } } * (\frac{a^{-\frac{1}{5} }}{b^{\frac{1}{20} }} )^{15} =[/tex]
[tex]\frac{(a^\frac{40}{4}) * (a^{-1}*b^{\frac{5}{3} } )^{\frac{3}{2} } } {a^{\frac{5}{2} } * b^{\frac{22}{8} } } * \frac{(a^{-\frac{1}{5} })^{15}} {(b^{\frac{1}{20} })^{15}} =[/tex]
[tex]\frac{a^8 * (a^{-1})^{\frac{3}{2} } * (b^{\frac{5}{3} } )^{\frac{3}{2} } } {a^{\frac{5}{2} } * b^{\frac{11}{4} } } * \frac{a^{-3 }} {b^{\frac{15}{20} }} = \\[/tex]
[tex]\frac{a^8 * a^{-\frac{3}{2} } * b^{\frac{5*3}{3*2} } } {a^{\frac{5}{2} } * b^{\frac{11}{4} } } * \frac{a^{-3 }} {b^{\frac{3}{4} }} =[/tex]
[tex]\frac{a^8 * a^{-\frac{3}{2} } * b^{\frac{5}{2} } *a^{-3 } } {a^{\frac{5}{2} } * b^{\frac{11}{4} } *b^{\frac{3}{4} } } =[/tex]
[tex]\frac{a^{(8-\frac{3}{2}-3) } * b^{\frac{5}{2} } } {a^{\frac{5}{2} } * b^{(\frac{11}{4}+ \frac{3}{4})} } =[/tex]
[tex]\frac{a^{\frac{7}{2} } * b^{\frac{5}{2} } } {a^{\frac{5}{2} } * b^{\frac{7}{2} } } =[/tex]
[tex]=a^{(\frac{7}{2}-\frac{5}{2})}* b^{(\frac{5}{2} -\frac{7}{2})}=[/tex]
[tex]=a* b^{-1}= \frac{a}{b}[/tex]
