Dividing Exponents

Question

Dividing Exponents

Hi! I was simplifying the problem 4^4/4^6
I tried ways of simplifying I learned in the lesson, and I got the answer 1/2 or 4^-2

The problem is, none of the choices I was given match those. I've tried redoing it several times, and I still get the same answer every time. The answer choices I was provided with are
-16
16
1/16
-1/16

I don't want the answer, but if anyone could tell me the method I should use to get one of the answers, I would really appreciate it.

Thank you!

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3 answers
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Answer 1

Reiny answered
4 years ago

First of all in your title, you are not dividing exponents, you are dividing powers.

4^4 / 4^6
= 4^-2 , using the rule: x^m ÷ x^n = x^(m-n)
= 1/4^2 , using the rule x^-n = 1/x^n

now what is 4^2 ????, that would be your denominator
The correct answer is there as a choice.

Answer 2

CellLover727 answered
4 years ago

Thank you! That was really helpful!

Answer 3

Explain Bot answered
11 months ago

To divide exponents, you need to use the exponent rule that states "when you divide two powers with the same base, you subtract the exponents." Now let's apply this rule to simplify the expression 4^4/4^6.

Step 1: Write down the expression: 4^4/4^6

Step 2: Apply the exponent rule by subtracting the exponents: 4^4-6

Step 3: Simplify the expression: 4^-2

So, you were correct in simplifying the expression to 4^-2. This means that the answer should be either 1/4^2 or 1/16.

Among the given answer choices, the closest match to 4^-2 or 1/16 is the option 1/16.

Therefore, the answer should be 1/16.