Odpowiedź:
1.
a)
[tex] {25}^{2} \times ( \frac{1}{5} ) ^{ - 3} = ( {5}^{2} )^{2} ) \times {5}^{3} = {5}^{4} \times {5}^{3} [/tex]
[tex] {5}^{4 + 3} = {5}^{7} [/tex]
b)
[tex]( {0.2})^{ - 4} \times {125}^{ - 3} \div {5}^{4} [/tex]
[tex]( \frac{1}{5} )^{ - 4} \times {125}^{ - 3} \div {5}^{4} [/tex]
[tex] {5}^{4} \times ( {5}^{3} )^{ - 3} ) \div {5}^{4} = {5}^{4} \times {5}^{ - 9} \div {5}^{4} =[/tex]
[tex] {5}^{4 + ( - 9)} \div {5}^{4} = {5}^{ - 5 - 4} = {5}^{ - 9} [/tex]
2.
a)
[tex]( \frac{2}{3} )^{4} = \frac{16}{81} = 0.197[/tex]
[tex]( \frac{2}{3} )^{5} = \frac{32}{243} = 0.131[/tex]
[tex]( \frac{2}{3} )^{4} > (\frac{2}{3} )^{5} [/tex]
b)
[tex] {6}^{ - 5} = \frac{1}{7776}[/tex]
[tex] {6}^{ - 4} = \frac{1}{1296} [/tex]
[tex] {6}^{ - 5} < {6}^{ - 4} [/tex]
c)
[tex]((0.02)^{ - 2} )^{ - 3} = 6.4 \times {10}^{ - 11} [/tex]
[tex]( {0.02})^{5} \times ( {0.02})^{2} = (3.2 \times 10^{ - 9}) \times \frac{1}{2500} [/tex]
[tex] = 1.28 \times 10^{ - 2} [/tex]
[tex]((0.02)^{ - 2} )^{ - 3} > (0.02)^{5} \times (0.02)^{2} [/tex]
3.
[tex]( \frac{1}{4})^{ - 2} \times {16}^{ - 7} = {4}^{2} \times ( {4}^{2} )^{ - 7} )[/tex]
[tex] {4}^{2} \times {4}^{ - 14} = {4}^{2 + ( - 14)} = {4}^{ - 12} [/tex]
odp. B