SATMathematics Practice Test 1

One approach is to express $\frac{8^x}{2^y}$ 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 $\frac{8^x}{2^y}$ gives $\frac{(2^3)^x}{2^y}$ which can be written as $\frac{2^{3x}}{2^y}$, since the numerator and denominator of $\frac{2^{3x}}{2^y}$ have a common base, this expression can be rewritten as $2^{3x-y}$. It is given that $3x-y=12$,so one can substitute 12 for the exponent,$3x-y$,giving that expression $\frac{8^x}{2^y}$ 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 $\frac{8^x}{2^y}$ can be determined.