Question

Solve:
1. 4/9 ÷ x = -10/3
2. (x^n/x^p)^m × (x^p/x^m)^n × (x^m/x^n)^p
3. 11^4x × 11^-3 = 11 × 121^4​

Answer 1

Required Answers:

1. $\sf \bf \: \dfrac{4}{9} ÷ x = - \dfrac{ - 10}{3}$

$\\ 1. \: \: \: \: \: \tt{\pmb \: \dfrac{4}{9} ÷ x = \dfrac{ - 10}{3}} \\ \\ \\ \tt\: \implies \: \: \: \dfrac{4}{9} \times \frac{1}{x} = \dfrac{ - 10}{3} \\ \\ \\ \implies \tt \: \dfrac{1}{x} = \dfrac{ - 10}{3} \div \frac{4}{9} \\ \\ \\ \implies \tt \: \dfrac{1}{x} = \dfrac{ - 10}{3} \times \frac{9}{4}\\ \\ \\ \implies \tt \: \dfrac{1}{x} = \dfrac{ \cancel{ - 10}}{ \cancel{3}} \times \frac{ \cancel{9}} {\cancel{4} } \\ \\ \\ \implies \tt \: \dfrac{1}{x} = \dfrac{ - 5}{1} \times \frac{3}{2 } \\ \\ \\ \implies \tt \: \dfrac{1}{x} = \dfrac{ - 15}{2}\\ \\ \\ \implies \tt \: {x}= \dfrac{ - 2}{15}$

________________________________________

$\sf \bf \: 2. \: \: \: {\bigg( \dfrac{ {x}^{n} }{ {x}^{p} } \bigg)}^{m} \times {\bigg( \dfrac{ {x}^{p} }{ {x}^{m} } \bigg)}^{n} \times {\bigg( \dfrac{ {x}^{m} }{ {x}^{n} } \bigg)}^{p}$

$\\ \tt \: \: 1. \: \: \: {\bigg( \dfrac{ {x}^{n} }{ {x}^{p} } \bigg)}^{m} \times {\bigg( \dfrac{ {x}^{p} }{ {x}^{m} } \bigg)}^{n} \times {\bigg( \dfrac{ {x}^{m} }{ {x}^{n} } \bigg)}^{p} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt\: = { \bigg( {x}^{n - p} } \bigg)^{m} \times { \bigg( {x}^{p- m} } \bigg)^{n} \times { \bigg( {x}^{m - n} } \bigg)^{p} \\ \\ \\ \tt = {x}^{nm - pm} \times \: {x}^{pn - mn} \times \: {x}^{mp - np} \\ \\ \\ = \tt \: {x}^{nm - pm + pn - mn + mp - np} \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \tt\: = {x} \: ^ {\cancel{nm - pm + pn - mn + mp - np}} \\ \\ \\ = \tt\: {x}^{0} \: \: \: \\ \\ \\ \tt \: \: \: \: = 1$

________________________________________

$\sf \bf\: \: \: 3. \: \: \: \: \: \: \: {11}^{4x + ( - 3)} = 11 \times {121}^{4}$

$\\ \tt \: \: \: 3. \: \: \: \: \: \: \: {11}^{4x + ( - 3)} = 11 \times {121}^{4} \\ \\ \\ \implies \tt\: {11}^{4x - 3} = {11}^{1} \times {11}^{8} \\ \\ \\ \tt \implies \: {11}^{4x - 3} = {11}^{(1 + 8)} \\ \\ \\ \tt \implies \: {11}^{4x - 3} = {11}^{9} \\ \\ \\ \: \: \: \: \: \: \: \: \: \tt \implies \: \cancel{11} \: ^{4x - 3} = \cancel{11} \: ^{9} \\ \\ \\ \: \: \: \: \: \: \: \: \tt \implies \: 4x - 3 = 9 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \tt \implies \: 4x = 9 + 3 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \implies4x = 12 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt \implies \: x = \frac{12}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies\tt \: x = 3$

________________________________________

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Hence Solved!!

⠀⠀⠀⠀⠀⠀⠀⠀⠀Hope it Helps uh :)