Question

50points guys


with explanation or will be reported​

Answer 1

SoLuTiOn :-

It is given 3x - y = 12

So,

$3x - y = 12 \\ \\ \implies 3x = 12 + y \\ \\ \implies x = \frac{12 + y}{3}$

$\frac{ {8}^{x} }{ {2}^{y} } \\ \\ putting \: x = \frac{12 + y}{3} \\ \\ = \frac{ {8}^{ \frac{12 + y}{3} } }{ {2}^{y} } \\ \\ = \frac{ {2}^{(3 \times \frac{12 + y}{3}) } }{ {2}^{y} } \\ \\ = \frac{ {2}^{12 + y} }{ {2}^{y} } \\ \\ = {2}^{12 + y - y} \\ \\ = {2}^{12}$

Option 'A' is correct..

Answer 2

Question :

If 3x-y = 12 ,what is the value $\frac{8{}^{x}}{2{}^{y}}$

Formulas :

$1)a {}^{m} \times a {}^{n} = a {}^{m + n}$

$2) \frac{a {}^{m} }{a {}^{n} } = a {}^{m - n}$

$3)a {}^{m} \times b {}^{m} = (ab) {}^{m}$

Solution :

Given: $\sf\:3x-y=12$

We have to find the value of $\frac{8{}^{x}}{2{}^{y}}$

_______________________

$\sf \dfrac{8 {}^{x} }{2 {}^{y} }$

$= \sf \dfrac{(2 {}^{3} ) {}^{x} }{2 {}^{y} }$

$= \sf \dfrac{2 {}^{3x} }{2 {}^{y} }$

we know that $\bf\:\frac{a{}^{m}}{a{}^{n}}=a{}^{m-n}$

$= \sf 2 {}^{3x - y}$

$\sf\:3x-y=12$ ( Given )

$= 2 {}^{12}$

Therefore, correct option is a)$\sf\:2{}^{12}$