Question

please answer my questions with explanation with clarity put it with photo please​

Answer 1

Question :–

$\\ \sf solve \: \: the \: \: following : {(81)}^{ - 4} \div {(729)}^{2 - x} = {(9)}^{4x}$

ANSWER :–

GIVEN :–

$\\ \sf \to {(81)}^{ - 4} \div {(729)}^{2 - x} = {(9)}^{4x}$

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

$\\ \sf \implies {(81)}^{ - 4} \div {(729)}^{2 - x} = {(9)}^{4x}$

$\\ \sf \implies \dfrac{ {(81)}^{ - 4}}{{(729)}^{2 - x} } = {(9)}^{4x}$

• We should write this as –

$\\ \sf \implies \dfrac{ {( {3}^{4} )}^{ - 4}}{{({3}^{6})}^{2 - x} } = {( {3}^{2} )}^{4x}$

$\\ \sf \implies \dfrac{ {( {3})}^{ -16 }}{{(3)}^{6(2 - x)} } = {( {3} )}^{8x}$

$\\ \sf \implies \dfrac{ {( {3})}^{ -16 }}{{(3)}^{12- 6x} } = {( {3} )}^{8x}$

$\\ \sf \implies{ {( {3})}^{ -16 }}{{(3)}^{ - 12 + 6x} } = {( {3} )}^{8x}$

$\\ \sf \implies{ {( {3})}^{ -16 - 12 + 6x }} = {( {3} )}^{8x}$

$\\ \sf \implies{ {( {3})}^{ 6x - 28}} = {( {3} )}^{8x}$

• Compare –

$\\ \sf \implies 6x - 28 = 8x$

$\\ \sf \implies 6x - 8x = 28$

$\\ \sf \implies - 2x = 28$

$\\ \sf \implies x = - \cancel \dfrac{ 28}{2}$

$\\ \large \implies{ \boxed{ \sf x = - 14}}$

Answer 2

${\underline{\underline{\sf {\red{Correct~Answer~ With~ Less~ Steps:-}}}}}$

$\sf {81}^{ - 4} \div {729}^{2 - x} = {9}^{4x} \\\\\sf ↦ {( {9}^{2}) }^{ - 4} \div {( {9}^{3}) }^{(2 - x)} = {9}^{4x} \\\\ {\boxed{\tt{Using \: identity \: { ({a}^{m} )}^{n} = {a}^{mn}}}} \\\\ ↦ \sf{9}^{ - 8} \div {9}^{6 - 3x} = {9}^{4x} \\\\ {\boxed{\tt{Using \: identity \: {a}^{m} \div {a}^{n} = {a}^{m - n}}}} \\\\↦\sf {9}^{ - 8 - (6 - 3x)} = {9}^{4x} \\\\↦ \sf {9}^{3x - 14} = {9}^{4x} \\\\ ↦\sf 3x - 14 = 4x \\\\↦ \sf 4x - 3x = - 14 \\\\</p><h2>↦ \sf \underline\purple{x = - 14}$