[tex]a) {2}^{2} \times {25}^{2} = (2 \times 25 {)}^{2} = {50}^{2} = 2500 \\ {16}^{2} \times {5}^{2} = (16 \times 5 {)}^{2} = {80}^{2} = 6400 \\ {2}^{4} \times {50}^{4} = (2 \times 50 {)}^{4} = {100}^{4} = 100000000 \\ {4}^{3} \times {25}^{3} = (4 \times 25 {)}^{3} = {100}^{3} = 1000000 \\ {35}^{2} \times {2}^{2} = (35 \times 2 {)}^{2} = {70}^{2} = 4900[/tex]
[tex]b)( - \frac{1}{4} {)}^{2} \times {16}^{2} = ( - \frac{1}{4} \times 16 {)}^{2} = ( - 4 {)}^{2} = 16 \\ ( - 2 \frac{1}{2} {)}^{3} \times ( - 4 {)}^{3} = ( - \frac{5}{2} \times - 4 {)}^{3} = {10}^{3} = 1000 \\ ( - 0.1 {)}^{5} \times {10}^{5} = ( - 0.1 \times 10 {)}^{5} = {1}^{5} = 1 \\ ( - 1.5 {)}^{2} \times ( - 8 {)}^{2} = ( - 1.5 \times - 8 {)}^{2} = ( - \frac{3}{2} \times - 8 {)}^{2} = {12}^{2} = 144[/tex]
[tex]c)( \frac{1}{6} {)}^{5} \times {12}^{5} = ( \frac{1}{6} \times 12 {)}^{5} = {2}^{5} = 32 \\ {7.5}^{3} \times ( \frac{2}{3} {)}^{3} = ( \frac{15}{2} \times \frac{2}{3} {)}^{3} = {5}^{3} = 125 \\ ( \frac{2}{7} {)}^{8} \times 3.5 {}^{8} = ( \frac{2}{7} \times \frac{7}{2} {)}^{8} = {1}^{8} = 1 \\ 0.7 {5}^{2} \times (2 \frac{2}{3} {)}^{2} = ( \frac{3}{4} \times \frac{8}{3} {)}^{2} = {2}^{2} = 4 \\ {10}^{3} \times 0.0 {1}^{3} = (10 \times 0.01 {)}^{3} = 0.1 {}^{3} = 0.001[/tex]
[tex] {2}^{3} \times {3}^{3} \times ( \frac{1}{6} {)}^{3} = (2 \times 3 \times \frac{1}{6} {)}^{3} = (6 \times \frac{1}{6} {)}^{3} = {1}^{3} = 1 \\ ( \frac{5}{3} {)}^{4} \times ( \frac{3}{4} {)}^{4} \times {4}^{4} = ( \frac{5}{3} \times \frac{3}{4} \times 4 {)}^{4} = {5}^{4} = 625 \\ 2.5 {}^{5} \times {4}^{5} \times 0. {2}^{5} = (2.5 \times 4 \times0.2 {)}^{5} = {2}^{5} = 32[/tex]
