Question

1) 2ⁿ-¹•4ⁿ-²•8ⁿ-3=
2)3²ⁿ+⁶:3ⁿ+⁸=
3)9³ⁿ+⁴:27²ⁿ+¹=
4)a⁵ⁿ-³•a⁴ⁿ+¹=
5)a²ⁿ+⁹•a³ⁿ+⁷=
6)b^k+⁵:b^k+⁴=

Answer 1

Ответ:

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

$2) {3}^{2n + 6} \div {3}^{n + 8} = {3}^{2n + 6 - n + 8} = {3}^{n + 14}$

$3) {9}^{3n + 4} \div {27}^{2n + 1} = ( { {3}^{2} })^{3n + 4} \div ({ {3}^{3} })^{2n + 1} = {3}^{6n + 8} \div {3}^{6n + 3} = {3}^{6n + 8 - 6n + 3} = {3}^{11}$

$4) {a}^{5n - 3} \times {a}^{4n + 1} = {a}^{5n - 3 + 4n + 1} = {a}^{9n - 2}$

$5) {a}^{2n + 9} \times {a}^{3n + 7} = {a}^{2n + 9 + 3n + 7} = {a}^{5n + 16}$

${b}^{k + 5} \div {b}^{k + 4} = {b}^{k + 5 - k + 4} = {b}^{9}$