Степениуване 6 клас

[Петя79]

Пресметнете:
а) 5^4 ×21^3/14^4 ×15^3
б) 10^5×55^4/5^9×22^4
в) 30^3×28^4/35^4×24^3

[S.B.]

Пресметнете:
а) 5^4 ×21^3/14^4 ×15^3
б) 10^5×55^4/5^9×22^4
в) 30^3×28^4/35^4×24^3

а)[tex]\frac{5^{4}.21^{3}}{14^{4}.15^{3}} = \frac{5^{4}.(3.7)^{3}}{(2.7)^{4}.(5.3)^{3}} = \frac{5^{4}.3^{3}.7^{3}}{2^{4}.7^{4}.5^{3}.3^{3}} = \frac{5}{2^{4}.7} = \frac{5}{16.7} = \frac{5}{112}[/tex]

б)[tex]\frac{10^{5}.55^{4}}{5^{9}.22^{4}} = \frac{(2.5)^{5}.(5.11)^{4}}{5^{9}.(2.11)^{4}} = \frac{2^{5}.5^{5}.5^{4}.11^{4}}{5^{9}.2^{4}.11^{4}} = 2[/tex]

в)[tex]\frac{30^{3}.28^{4}}{35^{4}.24^{3}} = \frac{(2.3.5)^{3}.(2^{2}.7)^{4}}{(5.7)^{4}.(2^{3}.3)^{3}} = \frac{2^{3}.3^{3}.5^{3}.2^{8}.7^{4}}{5^{4}.7^{4}.2^{9}.3^{3}} = \frac{2^{11}}{5.2^{9}} = \frac{2^{2}}{5} = \frac{4}{5}[/tex]