Question

Кто поможет решить, дам максимальное кол-во баллов!

Срочно, решить все!!! ​

Answer 1

$1. \: \: \: \: \: {5}^{n + 2} \times {5}^{2n + 1}$

$n + 2 + 2n + 1 = 3n + 3 = 3(n + 1)$

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${5}^{n + 2} \times {5}^{2n + 1} = {5}^{3(n + 1)}$

$2. \: \: \: \: \: {9}^{3n + 4} \div {27}^{2n + 1} = { {(3}^{2}) }^{3n + 4} \div { {(3}^{3} )}^{2n + 1} = {3}^{6n + 8} \div {3}^{6n + 3} = {3}^{5} = 243$

$3. \: \: \: \: \: { {(5}^{2} )}^{n} = {5}^{18} \\ {5}^{2n} = {5}^{18} \\ 2n = 18 \\ n = 9$

$4. \: \: \: \: \: {2}^{n - 1} \times {4}^{n - 2} \times {8}^{n - 3} = {2}^{n - 1} \times { {(2}^{2}) }^{n - 2} \times { {(2}^{3}) }^{n - 3} = {2}^{n - 1} \times {2}^{2n - 4} \times {2}^{3n - 9} = {2}^{6n - 14}$

$5. \: \: \: \: \: {4}^{3} \times {8}^{4} \times {16}^{5} = {2}^{n} \\ { {(2}^{2}) }^{3} \times { ({2}^{3} )}^{4} \times ({ {2}^{4}) }^{5} = {2}^{n} \\ {2}^{6} \times {2}^{12} \times {2}^{20} = {2}^{n} \\ {2}^{38} = {2}^{n \\ } \\ n = 38$