Zadanie 1
- [tex]15^{4} : 5^{4} = (15:5)^{4} = 3^{4} = 81[/tex], wzór nr 5
- [tex]5^{4} * 5^{2} = 5^{6}[/tex], wzór nr 1
- [tex]3^{4} : 2^{3} = 81 : 8 = 10\frac{1}{8}[/tex], brak wzoru
- [tex]3^{4} + 3^{2} = 81 + 9 = 90[/tex], brak wzoru
- [tex](3^{5})^{4} = 3^{20}[/tex], wzór nr 3
- [tex]5^{10} * 2^{10} = (5 * 2)^{10} = 10^{10}[/tex], wzór nr 4
- [tex]70^{8} : 7^{8} = (70:7)^{8} = 10^{8}[/tex], wzór nr 5
- [tex]5^{0} - 5^{2} = 1 - 25 = -24[/tex], brak wzoru
Zadanie 2
[tex]2^{6} * 5^{6} = (2*5)^{6} = 10^{6}[/tex]
[tex]4^{5} * 25^{5} = (4 * 25)^{5} = 100^{5}[/tex]
[tex]16^{10} * 0,125^{10} = (16*0,25)^{10} = 2^{10}[/tex]
Zadanie 3
[tex]8 = 2^{3}, wiec \ 8^{2} = (2^{3})^{2} = 2^{6}[/tex]
[tex]4 = 2^{2}[/tex], więc [tex]4^{2} = (2^{2})^{2} = 2^{4}[/tex]
[tex]27 = 3^{3}[/tex], więc [tex]27^{4} = (3^{3})^{4} = 3^{12}[/tex]
Zadanie 4
a) do kratki wpisz 15
b) [tex]81^{3} = (3^{4})^{3} = 3^{12}[/tex]
c) [tex]9^{12} = (3^{2})^{12} = 3^{24}[/tex]
Zadanie 5
[tex]3^{8} * 27^{5} = 3^{8} * (3^{3})^{5} = 3^{8} * 3^{15} = 3^{8+15} = 3^{23}[/tex]
[tex]\frac{27^{5} }{81^{3}} = \frac{(3^{3})^{5} }{(3^{4})^{3} } = \frac{3^{15} }{3^{12} } = 3^{3}[/tex]
[tex](27^{5} * 9^{12})^{3} = [(3^{3})^{5}*(3^{2})^{12}] ^{3} = 3^{45} * 3^{72} = 3^{117}[/tex]
