Question

$\huge\star\green{{Hey Mate...!! }}$
$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\blue{W}\green{E}\pink{R}}}}$it​

Answer 1

Question :

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

Formulas :

$\sf1)\:a^m\times\:a^n=a^{m+n}$

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

$\sf3)a^m\times\:b^m=(ab)^m$

Solution :

Given: $\sf3x-y=12$

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 $\bf\:\dfrac{a{}^{m}}{a{}^{n}}=a{}^{m-n}$

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

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

$= 2 {}^{12}$

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

Answer 2

Given:-

• 3x - y = 12

To Find :-

What is the value of $\frac{ {8}^{x} }{ {2}^{y} }$

Solution:-

$\sf \: \frac{ {8}^{x} }{ {2}^{y} } \\ \\ \sf \: \frac{ {2}^{3x} }{ {2}^{y} } \\ \\ \sf \: formula \: used \: here \\ \\ \sf \: {a}^{m - n} \\ \\ \sf \: {2}^{3x - y} \\ \\ \sf \: 3 x - y \: = \: 12 \\ \\ \sf \: {2}^{12}$

Hence, 2^12 is the value.