Exponent Rules Question 10

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

$ 10$

$ 2^{10}$

$ 3^{10}$

$9^{10}$

Approach

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.

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