Can someone explain why this happens? (Dividing variables with exponents) Alright, so let's say I

Emanuel Keith

Emanuel Keith

Answered question

2022-06-15

Can someone explain why this happens? (Dividing variables with exponents)
Alright, so let's say I have
x 6 x 4
The answer is 1 x 2 , but why isn't it 1 x 2 ??

Answer & Explanation

sleuteleni7

sleuteleni7

Beginner2022-06-16Added 28 answers

Let's think about what negative exponents really mean. Consider the following list
2 3 = 8
2 2 = 4
2 1 = 2
Notice that every time we decrease an exponent, we divide by 2. Continuing this list, we have that
2 3 = 8
2 2 = 4
2 1 = 2
2 0 = 1
2 1 = 1 / 2
2 2 = 1 / 4
Rather interesting, we see a pattern: 2 n = 1 2 n . Therefore there is no reason for a negative sign on the quantity itself, since we're successively dividing by positive numbers.
Emmy Knox

Emmy Knox

Beginner2022-06-17Added 10 answers

It might help you see what's going on if you write them as two story fractions:
x 6 x 4 = ( 1 x 6 ) ( 1 x 4 ) = 1 x 6 × x 4 1 by the reciprocal rule = 1 x 2 = 1 x 2
So you are correct, and the "answer" is wrong.]

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