Question

find the value of x/y if

$\tt( \dfrac{2}{7} ) ^{ - 6} \times ( \dfrac{14}{9} ) ^{ - 6} = ( \dfrac{x}{y} ) ^{ - 6}$
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Answer 1

$\huge \blue{ \star} \sf \: LETS \: UNDERSTAND \: THE \: QUESTION -$

This is the question of exponents and power in which we need to find the value of x/y if $\sf( \dfrac{2}{7} ) ^{ - 6} \times ( \dfrac{14}{9} ) ^{ - 6} = ( \dfrac{x}{y} ) ^{ - 6}$

So let's solve it !!

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$\huge \green{ \star} \sf \: ANSWER-$

$\Longrightarrow\tt \dfrac{x}{y} = \dfrac{4}{ 9}$

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$\huge \red{ \star} \sf \: EXPLANATION -$

$\longrightarrow\tt( \dfrac{2}{7} ) ^{ - 6} \times ( \dfrac{14}{9} ) ^{ - 6} = ( \dfrac{x}{y} ) ^{ - 6}$

$\longrightarrow\tt( \dfrac{2}{7} \times \dfrac{14}{9} ) ^{ - 6} = ( \dfrac{x}{y} ) ^{ - 6}$

$\longrightarrow\tt( \dfrac{2}{ \cancel{7}} \times \dfrac{ \cancel{14}}{9} ) ^{ - 6} = ( \dfrac{x}{y} ) ^{ - 6}$

$\longrightarrow\tt( \dfrac{4}{ 9} ) ^{ - 6} = ( \dfrac{x}{y} ) ^{ - 6}$

Now , the power are same . therefore , will cancel .

$\Longrightarrow\tt \dfrac{x}{y} = \dfrac{4}{ 9}$

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$\huge \orange{ \star} \sf \: LAWS \: OF \: EXPONENTS -$

if a/b and c/d are any non zero rational numbers and m and n are any integers , then we have

⠀

$: \Longrightarrow \: \sf {( \dfrac{a}{b} )}^{m} \times { (\dfrac{a}{b}) }^{n} = \bold { (\dfrac{a}{b} ) ^{m + n}}$

⠀

$: \Longrightarrow \: \sf {( \dfrac{a}{b} )}^{m} \div { (\dfrac{a}{b}) }^{n} = \bold { (\dfrac{a}{b} ) ^{m - n}}$

⠀

$: \Longrightarrow \: \sf {(( \dfrac{a}{b} )}^{m} ) ^{n} = \bold { (\dfrac{a}{b} ) ^{mn}}$

⠀

$: \Longrightarrow \: \sf {( \dfrac{a}{b} \times \dfrac{c}{d} )}^{m} = \bold { (\dfrac{a}{b}) ^{m}} \times \bold { (\dfrac{c}{d} ) ^{m }}$

⠀

$: \Longrightarrow \: \sf {( \dfrac{(a \div b)}{(c \div d) } )}^{m} = \bold { (\dfrac{a \div b}{c \div d} ) ^{m }}$

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$: \Longrightarrow \: \sf {( \dfrac{a}{b} )}^{0} = \bold {1}$

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$: \Longrightarrow \: \sf {( \dfrac{a}{b} )}^{ - n} = \bold { (\dfrac{b}{a} ) ^{n}}$ , when n is a positive integer .