If $3y-x=10$, what is the value of $\dfrac{27^y}{3^x}$ ?

Summary Submit

We should notice that $\dfrac{27^y}{3^y}$ might be simplifiable. To use any of the exponent rules, we must rewrite with equivalent bases.

$$\frac{27^y}{3^x}$$ $$=\frac{(3^3)^y}{3^x}$$ $$=\frac{3^{3y}}{3^x}$$ $$= 3^{3y-x}$$ $$=\boxed{3^{10}}$$