Question

Solve the following: (81)^-4 ÷ (729)^2-x = 9^4x

Answer 1

Answer:

$\frac{ {(81)}^{ - 4} }{ {(729)}^{2 - x} } = {(9)}^{4x} \\ \\ \frac{ {( {3}^{4} )}^{ - 4} }{ {( {3}^{6} )}^{2 - x} } = {( {3}^{2} )}^{4x} \\ \\ \frac{ {(3)}^{ - 16} }{ {(3)}^{12 - 6x} } = {(3)}^{8x} \\ \\ {(3)}^{ - 16 - (12 - 6x)} = {(3)}^{8x} \\ \\ {3}^{ - 28 + 6x} = {3}^{8x} \\ \\ \color{blue}{ \underline{on \:comparing : }} \\ - 28 + 6x = 8x \\ - 28 = 2x \\ \boxed{x = - 14} \\ \\\red{\mathfrak{ \large{\underline{{Hope \: It \: Helps \: You}}}}} \\ \blue{\mathfrak{ \large{\underline{{Mark \: Me \: Brainliest}}}}}$

Answer 2

Step-by-step explanation:

${81}^{ - 4} \div {729}^{2 - x} = {9}^{4x} \\ {(81)}^{ - 4} \div {(729)}^{2 - x} = {(9)}^{4x} \\ {( {9}^{2} )}^{ - 4} \div {( {9}^{3}) }^{2 - x} = {9}^{4x} \\ {9}^{(2)( - 4)} \div {9}^{(3)(2 - x)} = {9}^{4x} \\ {9}^{ - 8} \div {9}^{6 - 3x} = {9}^{4x} \\ {9}^{ (- 8 )- (6 - 3x)} = {9}^{4x} \\ {9}^{ ( - 8 - 6 + 3x)} = {9}^{ 4x} \\ {9}^{( - 14 + 3x)} = {9}^{4x} \\ \\ \\ - 14 + 3x = 4x \\ \: - 14 = 4x - 3x \\ - 14 = x$

Hence ,

the value of x = -14