1.
[tex] {( - 1 \frac{2}{3})}^{2} = {( - \frac{5}{3}) }^{2} = \frac{25}{9} = 2 \frac{7}{9} [/tex]
Odp. D
2.
[tex] {10}^{ - 3} = {( \frac{1}{10}) }^{3} = \frac{1}{1000} = 0.001[/tex]
Odp. C
3.
[tex] \frac{ {5}^{10} }{ {5}^{4} \times 5 } = \frac{ {5}^{10} }{ {5}^{5} } = {5}^{5} [/tex]
Odp. B
4.
[tex] {125}^{4} = ( { {5}^{3} )}^{4} = {5}^{12} [/tex]
[tex]25 = {5}^{2} [/tex]
[tex] {5}^{12} \times {5}^{2} = {5}^{14} [/tex]
Odp. C
5.
[tex] {4}^{88} = ({ {2}^{2}) }^{88} = {2}^{176} [/tex]
[tex] {2}^{88} \times {2}^{88} = {2}^{176} [/tex]
Odp. B
6.
[tex] {81}^{56} = ( { {3}^{4} )}^{56} = {3}^{224} [/tex]
[tex] {9}^{100} = ({ {3}^{2}) }^{100} = {3}^{200} [/tex]
[tex] {27}^{72} = ({ {3}^{3} )}^{72} = {3}^{216} [/tex]
Odp. A
7.
[tex] \frac{ {4}^{3} \times {8}^{2} }{ {2}^{5} \times {2}^{0} } \div {2}^{5} = \frac{ { ({2}^{2}) }^{3} \times { ({2}^{3} )}^{2} }{ {2}^{5} \times 1 } \div {2}^{5} = \frac{ {2}^{6} \times {2}^{6} }{ {2}^{5} } \div {2}^{5} = \frac{ {2}^{12} }{ {2}^{5} } \div {2}^{5} = {2}^{7} \div {2}^{5} = {2}^{2} [/tex]
Odp. B
8.
[tex] \frac{ {x}^{7} \times {x}^{3} \div {x}^{2} }{ {x}^{4} } \div {x}^{3} = \frac{ {x}^{10} \div {x}^{2} }{ {x}^{4} } \div {x}^{3} = \frac{ {x}^{8} }{ {x}^{4} } \div {x}^{3} = {x}^{4} \div {x}^{3} = x[/tex]
Odp. B
9. Odp. B
10. a)
[tex] \frac{ {5}^{4} + {5}^{4} + {5}^{4} + {5}^{4} + {5}^{4} }{ {5}^{3} } = \frac{5 \times {5}^{4} }{ {5}^{3} } = \frac{ {5}^{5} }{ {5}^{3} } = {5}^{2} = 25[/tex]
b)
[tex] \frac{ {3}^{4} \times {9}^{4} }{ {9}^{5} \div {27}^{2} } \div 81 = \frac{ {3}^{4} \times ( { {3}^{2}) }^{4} }{ { ({3}^{2}) }^{5} \div ( { {3}^{3} )}^{2} \div } \div {3}^{4} = \frac{ {3}^{4} \times {3}^{8} }{ {3}^{10} \div {3}^{6} } \div {3}^{4} = \frac{ {3}^{12} }{ {3}^{4} } \div {3}^{4} = {3}^{8} \div {3}^{4} = {3}^{4} = 81[/tex]
c)
[tex] \frac{ {(1 \frac{2}{3})}^{3} \times \frac{9}{25} }{( { { \frac{3}{5}) }^{3} )}^{2} } \div {(2 \frac{7}{9}) }^{3} = \frac{ {( \frac{5}{3}) }^{3} \div \frac{25}{9} }{ {( \frac{3}{5}) }^{6} } \div {( \frac{25}{9})}^{3} = \frac{ {( \frac{5}{3}) }^{3} \div {( \frac{5}{3}) }^{2} }{ (\frac{3}{5})^{6} } \div ( {( { \frac{5}{3} )}^{2}) }^{3} = \frac{ \frac{5}{3} }{ { (\frac{3}{5}) }^{6} } \div {( \frac{5}{3})}^{6} = \frac{ \frac{5}{3} \div ( { \frac{5}{3}) }^{6} }{ (\frac{3}{5})^{6} } = \frac{ { (\frac{5}{3}) }^{ - 5} }{( { \frac{3}{5} )}^{6} } = \frac{ { (\frac{3}{5}) }^{5} }{ { (\frac{3}{5}) }^{6} } = { (\frac{3}{5}) }^{ - 1} = \frac{5}{3} = 1 \frac{2}{3} [/tex]
11.
[tex] {2}^{3} = 8[/tex]
[tex] {( - 2)}^{3} = - 8[/tex]
[tex] {( - \frac{1}{2} )}^{3} = - \frac{1}{8} [/tex]
[tex] {( - 2)}^{0} = 1[/tex]
[tex] { - 2}^{0} = - 1[/tex]
[tex] {0}^{2} = 0[/tex]
[tex]{( - 2)}^{3} < { - 2}^{0} < {( - \frac{1}{2}) }^{3} < {0}^{2} < {( - 2)}^{0} < {2}^{3} [/tex]
12.
[tex]1000000 = {10}^{6} [/tex]
[tex]0.2 \times {10}^{ - 6} \times {10}^{6} = 0.2m[/tex]
[tex]0.2m = 0.2 \times 100cm = 20cm[/tex]
