Question

If 3x-y=123x−x=123, x, minus, y, equals, 12, what is the value of \frac{8^x}{2^y} 2 y 8 x ​ start fraction, 8, start superscript, x, end superscript, divided by, 2, start superscript, y, end superscript, end fraction

Answer 1

Answer:

$\frac{8^x}{2^y}$ = 4096

Step-by-step explanation:

Rules:

1. $\frac{a^m}{a^n}=a^{m-n}$
2. $a^m\times a^n= a^{m+n}$
3. $(a^m)^n=a^{m\times n}$

Given that,

3x-y =12

Therefore

$\frac{8^x}{2^y}$

$=\frac{(2^3)^x}{2^y}$  [ since $8=2^3$ ]

$=\frac{2^{3x}}{2^y}$   [ applying 3rd rule]

$=2^{3x-y}$ [ applying 2nd rule]

$=2^{12}$   [ since 3x-y =12]

=4096