Question

X upon Y equal to minus 1 upon 3 raise to the power minus 3 divided by 2 upon 3 to the power minus 4 find the value of x and y​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{ \frac{x}{y} = \frac{ {( \frac{1}{3} )}^{ - 3} }{{( \frac{2}{3} )}^{ - 4} } }$

TO DETERMINE

The value of x and y

EVALUATION

$\displaystyle \sf{ \frac{x}{y} = \frac{ {( \frac{1}{3} )}^{ - 3} }{{( \frac{2}{3} )}^{ - 4} } }$

$\displaystyle \sf{ \implies \: \frac{x}{y} = \frac{ ({ {3}^{ - 1} )}^{ - 3} }{{( \frac{3}{2} )}^{ 4} } }$

$\displaystyle \sf{ \implies \: \frac{x}{y} = \frac{ ({ {3}^{ 3} )}}{{( \frac{3}{2} )}^{ 4} } }$

$\displaystyle \sf{ \implies \: \frac{x}{y} = \frac{ {3}^{3} \times {2}^{4} }{ {3}^{4} } }$

$\displaystyle \sf{ \implies \: \frac{x}{y} = \frac{ {2}^{4} }{ {3}^{4 - 3} } }$

$\displaystyle \sf{ \implies \: \frac{x}{y} = \frac{ {2}^{4} }{ {3}^{1} } }$

$\displaystyle \sf{ \implies \: \frac{x}{y} = \frac{ 16 }{3} }$

Comparing we get

x = 16k and y = 3k with k ≠ 0

Taking k = 1 we get

x = 16 & y = 3

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Answer 2

Step-by-step explanation:

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