If 3x  y = 12, what is the value of
\[ \frac{8^x}{2^y}\]

\[ A) 2^{12} \]

\[ B) 4^{4} \]

\[ C) 8^{2} \]

D) Cannot be determined from the given information.

Answer:
As we know we can manipulate exponents with the same base. Since 2 and 8 are both powers of 2, substituting 2^3 for 8 in the numerator of
As we know we can manipulate exponents with the same base. Since 2 and 8 are both powers of 2, substituting 2^3 for 8 in the numerator of
\[ \frac{8^x}{2^y}\]

gives us
\[ \frac{(2^3)^x}{2^y}\]

Since the numerator and denominator of have a common base, i.e. 2, this expression can be rewritten as
\[ \frac{(2^{3x})}{2^y}\]

\[ 2^{3xy}\]

We are given that 3x−y=12, so one can substitute 12 for the exponent, 3x−y, so the expression
\[ \frac{8^x}{2^y}\]

can be reduced to
\[ 2^{12}\]

The final answer is A.