Question

pls sove 11, 12, 13 and 14
50 points are there
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Answer 1

Answer:

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Answer}}}}}}$

▬▬▬▬▬ஜ۩۞۩ஜ▬▬▬▬▬▬

11:- So first you have to distribute it.

ay . az . bz . by . bx . cx . cz . cx . cy

So cancel the Common ones

Answer: a x-z . b y-x . c z-y

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Answer 2

Answer:

➡➡your ans

$\bf\ 11:- So \: first \: you \: have \: to \: distribute \: it. \\ \\ </h2><h2></h2><h2> \bf\ ay . az . bz . by . bx . cx . cz . cx . cy \\ \\ </h2><h2></h2><h2> \bf\ So \: cancel \: the \: Common \: ones \: \\ \\ </h2><h2></h2><h2> \bf\red{ Answer: a x-z . b y-x . c z-y}$

$\bf\ \hookrightarrow \: using \: formula \\ \\ \bf\red{ a) \implies: {a}^{m} + {a}^{n} = {a}^{m + n} } \\ \\ \bf\green{b) \implies: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} } \\ \\ \\\bf\pink{ \underline{ c) \implies: { {a}^{m} }^{n} = {a}^{m \times n} } }\\ \\ \bf\ \: 12 ) \frac{ {x}^{2n + 3 }. {x}^{(2n + 1)(n + 1)} }{ {x}^{ {3}^{(2n + 1)} }. {x}^{ {n}^{(2n + 1)} } } \\ \\ \bf\ \implies: \frac{ {x}^{2n + 3 + (2n + 1)(n + 1)} }{ {x}^{6n + 3} . {x}^{ {2n}^{2} + n } } \\ \\ \bf\ \implies: \frac{ {x}^{2n + 3 + {2n}^{2} + 2n + n + 1 } }{ {x}^{6n + 3 + {2n}^{2} + n} } \\ \\ \bf\ \implies: \frac{ {x}^{ {2n}^{2} + 5n + 3 } }{ {x}^{ {2n}^{2} + 7n + 3} } \\ \\ \bf\ \implies: {x}^{ {2n}^{2} + 5n + 3 - {2n}^{2} - 7n - 3 } \\ \\ \bf\ \implies: {x}^{ - 2n}$

$\bf\ 13)\frac{ {a}^{7 + 2n}. {a}^{ {2}^{(3n + 2)}} }{ {a}^{ {4}^{(2n + 3)} } } \\ \\ \bf\ \implies: \frac{ {a}^{7 + 2n} . {a}^{6n + 4} }{ {a}^{8n + 13} } \\ \\ \bf\ \implies: \frac{ {a}^{(7 + 2n) + (6n + 4)} }{ {a}^{8n + 13} } \\ \\ \bf\ \implies: {a}^{7 + 2n + 6n + 4 - 8n - 13} \\ \\ \bf\ \implies: {a}^{8n - 8n + 11 - 13} \\ \\ \bf\ \implies: {a}^{ - 2}$

$\bf\ 14)a) {( \frac{81}{16}) }^{ \frac{ - 1}{4} } \\ \\ \bf\ \implies: { \frac{ ({3}^{4}) }{( {2}^{4} )} }^{ \frac{ - 1}{4} } \\ \\ \bf\ \implies: {( \frac{3}{2} )}^{4 \times \frac{ - 1}{4} } \\ \\ \bf\ \implies: { \frac{3}{2} }^{ - 1} \\ \\ \bf\ \implies: \frac{2}{3}$

$\bf\ 14)b) {64}^{ \frac{2}{3} } + \sqrt[3]{125} + {3}^{0} + \frac{1}{ {2}^{ - 5} } + {27}^{ \frac{ - 2}{3} } \\ \\ \bf\ \implies: {(4)}^{ {3}^.{ \frac{2}{3} } } + 5 + 1 + {2}^{5} + {5}^{ {3}^.{ \frac{ - 2}{3} } } \\ \\ \bf\ \implies: {4}^{2} + 5 + 1 + {2}^{5} + {3}^{ - 2} \\ \\ \bf\ \implies: \frac{ 486+ 1}{9} \\ \\ \bf\ \implies: \frac{487}{9} \\ \\ \bf\ 14)c) \sqrt{ \frac{ {y}^{3} }{x} } \times \sqrt{ \frac{y}{x} } \\ \\ \bf\ \implies: \sqrt{ \frac{ {y}^{4} }{ {x}^{2} } } \\ \\ \bf\ \implies: {y}^{2}$

$\bf\ 15) \frac{ { \frac{ - 3}{11} }^{(x + 5)} }{ { \frac{ - 3}{11} }^{ (- 2x + 3} )} = { \frac{ - 3}{11} }^{(2x - 5)} \times { \frac{ - 3}{11} }^{ { - 2}^{(x + 4)} } \\ \\ \bf\ \implies: { \frac{ - 3}{11} }^{x + 5 + 2x - 3} = { \frac{ - 3}{11} }^{2x - 5 - 2x - 8} \\ \\ \bf\ \implies: 3x + 2 = - 13 \\ \\ \bf\ \implies: 3x = - 15 \\ \\ \bf\ \implies: x = \frac{ - 15}{3} \\ \\ \bf\ \implies: x = - 5 \\ \\ \large\boxed{ \fcolorbox{red}{blue}{hope \: it \: help \: you}}$