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

Solve the following equation:

axay+a2ax= \frac{a^x}{a^y}+\frac{a^2}{a^x}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Simplify the following problem
00:03 When dividing powers with equal bases
00:07 The power of the result equals the difference between the exponents
00:11 We'll apply this formula to our exercise, and subtract the powers
00:15 This is the solution

Step-by-step written solution

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1

Understand the problem

Solve the following equation:

axay+a2ax= \frac{a^x}{a^y}+\frac{a^2}{a^x}=

2

Step-by-step solution

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

cmcn=cm−n \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:

axay+a2ax=ax−y+a2−x \frac{a^x}{a^y}+\frac{a^2}{a^x}=a^{x-y}+a^{2-x} Therefore the correct answer is A.

3

Final Answer

ax−y+a2−x a^{x-y}+a^{2-x}

Practice Quiz

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\( 112^0=\text{?} \)

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