SATMathematics Practice Test 1

One approach is to express $\frac{8^{\mathit{x}}}{2^{\mathit{y}}}$ so that the numerator and denominator are expressed with the same base.
Since 2 and 8 are both powers of 2, substituting $2^3$ for 8 in the numerator of $\frac{8^{\mathit{x}}}{2^{\mathit{y}}}$ gives $\frac{{\left(2^3\right)}^{\mathit{x}}}{2^{\mathit{y}}}$ which can be written as $\frac{2^{3\mathit{x}}}{2^{\mathit{y}}}$,
since the numerator and denominator of $\frac{2^{3\mathit{x}}}{2^{\mathit{y}}}$ have a common base, this expression can be rewritten as $2^{3\mathit{x}-\mathit{y}}$.
It is given that $3\mathit{x}-\mathit{y}=12$,so one can substitute 12 for the exponent,$3\mathit{x}-\mathit{y}$,giving that expression $\frac{8^{\mathit{x}}}{2^{\mathit{y}}}$ is equal to $2^{12}$
Choices B and C are incorrect because they are not equal to $2^{12}$.Choice D is incorrect because the value of $\frac{8^{\mathit{x}}}{2^{\mathit{y}}}$ can be determined.