Oblicz...- Zadanie 1: Matematyka w punkt 8

Rozwiązanie

$24 2^{5} : 12 1^{5} = (242 : 121)^{5} = 2^{5} = 32$

$\frac{1 2 ^{5} \cdot 1 2 ^{0}}{1 2 ^{3}} = 1 2^{5 + 0 - 3} = 1 2^{2} = 144$

$\frac{5 ^{8} : 5 ^{3} \cdot 5 ^{2}}{1 5 ^{2} \cdot ( \frac{1}{3} ) ^{2}} = \frac{5 ^{8 - 3 + 2}}{( 15 \cdot \frac{1}{3} ) ^{2}} = \frac{5 ^{7}}{5 ^{2}} = 5^{7 - 2} = 5^{5} = 3125$

$\frac{( 2 ^{3} \cdot 3 ^{4} ) ^{2}}{6 ^{4} \cdot 3 ^{2}} = \frac{( 2 ^{3} ) ^{2} \cdot ( 3 ^{4} ) ^{2}}{( 2 \cdot 3 ) ^{4} \cdot 3 ^{2}} = \frac{2 ^{6} \cdot 3 ^{8}}{2 ^{4} \cdot 3 ^{4} \cdot 3 ^{2}} = \frac{2 ^{6} \cdot 3 ^{8}}{2 ^{4} \cdot 3 ^{6}} = 2^{6 - 4} \cdot 3^{8 - 6} = 2^{2} \cdot 3^{2} = 4 \cdot 9 = 36$

$\frac{4 ^{3} + 4 ^{3} + 4 ^{3} + 4 ^{3}}{2 ^{4}} = \frac{4 ^{3} ( 1 + 1 + 1 + 1 )}{2 ^{4}} = \frac{4 ^{3} \cdot 4}{2 ^{4}} = \frac{4 ^{4}}{2 ^{4}} = (\frac{4}{2})^{4} = 2^{4} = 16$