Question

3.34. Упростите выражение: 1 1) 4y2 у"; 2) 5(2y'); 3) 2 ° : (бу° ); 4) 0,4y® : (3 уу. 32​

Answer 1

1)

$4 {y}^{2} \times \frac{1}{32} \times {y}^{4} = \frac{4 {y}^{2} \times {y}^{4} }{32} = \frac{ {y}^{(2 + 4)} }{8} = \frac{ {y}^{6} }{8}$

2)

$5 {(2 {y}^{2} )}^{3} = 5 \times {2}^{3} \times {( {y}^{2} )}^{3} = 5 \times 8 \times {y}^{(2 \times 3)} = 40 {y}^{6}$

3)

$2\frac{1}{2} \: {y}^{5} \div {(5 {y}^{2} )}^{2} = \frac{5}{2} \: {y}^{5} \div ( {5}^{2} \times {y}^{(2 \times 2)} ) = \frac{5 {y}^{5} }{2} \div 25 {y}^{4} = \frac{5 {y}^{5} }{2} \times \frac{1}{25 {y}^{4} } = \frac{5 {y}^{5} }{25 {y}^{4} } = \frac{1}{5} \: {y}^{(5 - 4)} = \frac{1}{5} \: {y}^{1} = \frac{1}{5} \: y \: \: \: или \: \: \: \frac{y}{5}$

4)

$0.4 {y}^{3} \div {(3 \frac{1}{5} {y}^{3} )}^{2} = \frac{4}{10} \: {y}^{3} \div {( \frac{16}{5} \: {y}^{3} )}^{2} = \frac{2}{5} \: {y}^{3} \div ( {( \frac{16}{5} )}^{2} \: {y}^{(3 \times 2)} ) = \frac{2 {y}^{3} }{5} \div ( \frac{256}{25} \: {y}^{6} ) = \frac{2 {y}^{3} }{5} \div \frac{256 {y}^{6} }{25} = \frac{2 {y}^{3} }{5} \times \frac{25}{256 {y}^{6} } = \frac{2 \times {y}^{3} \times 25}{5 \times 256 \times {y}^{6} } = \frac{5 }{128 \times {y}^{3} }$