Question

СРОЧНО! даю 30 баллов

Answer 1

Ответ:

1.

$- 3 {x}^{2} + 7 = - 3 \times {( - 5)}^{2} + 7 = - 3 \times 25 + 7 = - 75 + 7 = - 68$

2.

${a}^{8} \times {a}^{16} = {a}^{8 + 16} = {a}^{24} \\ {a}^{16} \div {a}^{4} = {a}^{16 - 4} = {a}^{12} \\ ( { {a}^{3} )}^{5} = {a}^{3 \times 5} = {a}^{15} \\ {(2a)}^{3} = {2}^{3} {a}^{3} = 8 {a}^{3}$

3.

$3 {a}^{2} b \times ( - 2 {a}^{3} {b}^{4} ) = 3 \times ( - 2) {a}^{2 + 3} {b}^{1 + 4} = - 6 {a}^{5} {b}^{5}$

$( - 3 {a}^{3} {b}^{2} )^{3} = {( - 3)}^{3} {a}^{3 \times 3} {b}^{2 \times 3} = - 27 {a}^{9} {b}^{6}$

4.

$y = {x}^{2}$

График во вложении

5.

$\frac{ {49}^{4} \times {7}^{5} }{ {7}^{12} } = \frac{ ({7}^{2})^{4} \times {7}^{5} }{ {7}^{12} } = \frac{ {7}^{2 \times 4} \times {7}^{5} }{ {7}^{12} } = \\ \frac{ {7}^{8} \times {7}^{5} }{ {7}^{12} } = \frac{ {7}^{8 + 5} }{ {7}^{12} } = \frac{ {7}^{13} }{ {7}^{12} } = {7}^{13 - 12} = 7$

6.

$4 \frac{1}{6} {a}^{8} {b}^{5} \times ( - 1 \frac{1}{5} {a}^{5} b)^{3} = \\ \frac{6 \times 4 + 1}{6} {a}^{8} {b}^{5} \times ( - \frac{5 \times 1 + 1}{5} {a}^{5} b)^{3} = \\ \frac{25}{6} {a}^{8} {b}^{5} \times ( - \frac{6}{5} {a}^{5} b) ^{3} = \\ \frac{25}{6} {a}^{8} {b}^{5} \times ( - \frac{6}{5} )^{3} {a}^{5 \times 3} {b}^{1 \times 3} = \\ \frac{25}{6} {a}^{8} {b}^{5} \times ( - \frac{216}{125} {a}^{15} {b}^{3}) = \\ \frac{25}{6} \times ( - \frac{216}{125} ) {a}^{8 + 15} {b}^{5 + 3} = \\ - \frac{36}{5} {a}^{23} {b}^{8} = - 7 \frac{1}{2} {a}^{23} {b}^{8}$

${a}^{m + 1} \times a \times {a}^{3 - m} = {a}^{m + 1 + 1 + 3 - m} = {a}^{5}$