Question

Find the value of 'm' for which (7/12)^-4 x (12/7)^-3m = (7/12)^8

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Answer 1

Answer:

Step-by-step explanation:

(7/12)^-4 x (7/12)^3m = (7/12)^8

(7/12)^3m-4 = (7/12)^8

3m-4 = 8

3m = 8 + 4

3m = 12

m = 3

Answer 2

$\sf{( { \frac{7}{12} })^{ - 4} \times( { \frac{12}{7} })^{ - 3m} = ({ \frac{7}{12} })^{8} }$

$\sf{ \to \color{grey}\: since \: bases \: are \: same \: power\: gets \: added \: when \: multiplied}$

$\sf{ \to ({ \frac{7}{12} })^{ - 4} \times ({ \frac{7}{12}})^{3m} = ( { \frac{7}{12} })^{8}} \\ \\ \sf{ \to( { \frac{7}{12} })^ \color{aqua}{ - 4 + 3m} } = ({ \frac{7}{12} })^ \color{blue}{8}$

$\sf{ \to \color{magenta}\: comapre \: the \: powers}$

- 4+3m = 8

3m= 8+4

3m = 12

m= 12/3

m= 4

so the value of m is 4.

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More information!!

$\sf{ \to \: {x}^{m} \times { {y}^{m} }= {xy}^{m} }$

$\sf{ \to \: {x}^{m} \times {x}^{n} = {x}^{m + n} }$

$\sf { \to \: {x}^{0} = 1}$

$\sf{ \to { \frac{ { x}^{m} }{ {x}^{n} } = {x}^{m - n} }}$

$\sf{ \to \: ( {x {}^{n} )}^{m } } = {x}^{m.n}$

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