Power of a Quotient Rule for Exponents: Variables in the exponent of the power

Solve the following:

$\frac{a^{xy}}{a^{3xy}}-a^{2xy}$

Keep in mind that in the question there is a fraction containing identical terms in its numerator and denominator. Therefore, we can use the distributive property of division to solve the exercise:

$\frac{c^m}{c^n}=c^{m-n}$
We apply this to our problem and simplify the first term:

$\frac{a^{xy}}{a^{3xy}}-a^{2xy}=a^{xy-3xy}-a^{2xy}=a^{-2xy}-a^{2xy}$

In the second step, calculate the result of the subtraction operation in the exponent to obtain:

$a^{-2xy}-a^{2xy}$

Therefore, the correct answer is D.

$a^{-2xy}-a^{2xy}$

Solve for a:

$\frac{a^{3b}}{a^{2b}}\times a^b=$

$a^{2b}$

Complete the exercise:

$\frac{a^{7+x}}{a^{10-2x}}$

$a^{-3+3x}$

Solve the exercise:

$\frac{a^{2x}}{a^y}\times\frac{a^{2y}}{a^{-y}}=$

$a^{2(x+y)}$