Solve the Exponential Expression: a^x/a^y + a^2/a^x

Question

Solve the following equation:

$\frac{a^x}{a^y}+\frac{a^2}{a^x}=$

00:00 Simply

00:03 When dividing powers with equal bases

00:07 The power of the result equals the difference of exponents

00:11 We'll use this formula in our exercise, and subtract the powers

00:15 And this is the solution to the question

We will apply the law of exponents for division between terms with identical bases:

$\frac{c^m}{c^n}=c^{m-n}$ Note: This law is only effective when the division is between terms with identical bases.

Let's return to the problem and apply the above law of exponents to each term in the sum separately:

$\frac{a^x}{a^y}+\frac{a^2}{a^x}=a^{x-y}+a^{2-x}$ Therefore the correct answer is A.

$a^{x-y}+a^{2-x}$