why do negative exponents become fractions

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https://www.quora.com/Why-do-negative-exponents-become-fractions?share=1

Why do negative exponents become fractions? – Quora
https://www.quora.com/Why-do-negative-exponents-become-fractions?share=1
Negative exponents are equivalent to fractions, because fractions represent division. What are normal or positive exponents? They are a way of representing multiplication. What is the opposite of multiplication?

https://study.com/academy/lesson/changing-negative-exponents-to-fractions.html

Changing Negative Exponents to Fractions – Math Class …
https://study.com/academy/lesson/changing-negative-exponents-to-fractions.html
It’s the opposite of multiplication: division. A negative exponent leads to the inverse of a number. In other words, a ^- n = 1/ a ^ n. 3^-2 isn’t 3 * 3, but 1/3^2. This is how we change negative…

https://math.stackexchange.com/questions/1882509/unresolved-why-does-negative-exponent-turns-into-a-fraction

Unresolved,why does negative exponent turns into a fraction?
https://math.stackexchange.com/questions/1882509/unresolved-why-does-negative-exponent-turns-into-a-fraction
Why it is turning into a fraction and also why it positive fraction? Why minus is vanished? algebra-precalculus intuition. Share. Cite. Follow asked Aug 4 ’16 at 17:19. … this is how we must extend exponentiation to negative exponents. Of course, there is more work to make sure this definition actually works.

https://findanyanswer.com/why-are-negative-powers-fractions

Why are negative powers fractions?
https://findanyanswer.com/why-are-negative-powers-fractions
Similarly, why do negative exponents become fractions? A negative exponent involves taking the inverse of the number, then multiplying it by itself once it’s in the denominator of the fraction. If the negative exponent is in the denominator already, we still do the inverse, which means moving the term to the numerator.

https://answers.yahoo.com/question/index?qid=20100302105733AAP6R8E

Why are negative exponents fractions? | Yahoo Answers
https://answers.yahoo.com/question/index?qid=20100302105733AAP6R8E
Why are negative exponents fractions? I was going through my old Algebra I to review some stuff before starting Algebra II and came across this section. The book does a pretty good job explaining HOW to simplify and solve negative exponents, but it doesn’t really explain WHY negative exponents become fractions.

https://study.com/academy/lesson/negative-exponents-writing-powers-of-fractions-and-decimals.html

Negative Exponents: Writing Powers of Fractions and …
https://study.com/academy/lesson/negative-exponents-writing-powers-of-fractions-and-decimals.html
They still indicate how many times to multiply a number to itself, but it also means that the base is on the wrong side of the fraction line, which means that if the negative exponent is in the…

https://magoosh.com/math/math-practice-negative-and-fractional-exponents/

Math Practice: Negative and Fractional Exponents – Magoosh
https://magoosh.com/math/math-practice-negative-and-fractional-exponents/
Negative exponents translate to fractions. For example, 4 -3 = 1/ (4 3) = 1/64. The more negative the exponent, the smaller the value. This is especially important in the sciences when talking about orders of magnitude (how big or small things are).

https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-pos-neg-exponents/v/negative-exponents

Negative exponents (video) | Khan Academy
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-pos-neg-exponents/v/negative-exponents
Learn how to rewrite expressions with negative exponents as fractions with positive exponents. A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ. For example, 2⁻⁴ = 1 / (2⁴) = 1/16.

https://www.purplemath.com/modules/exponent2.htm

Negative Exponents | Purplemath
https://www.purplemath.com/modules/exponent2.htm
A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For instance, x-2 (pronounced as ecks to the minus two) just means x2, but underneath, as in frac {1} {x^2} x21

https://www.sparknotes.com/math/algebra2/exponentialfunctions/section1/

Exponential Functions: Negative and Fractional Exponents …
https://www.sparknotes.com/math/algebra2/exponentialfunctions/section1/
A negative fractional exponent works just like an ordinary negative exponent. First, we switch the numerator and the denominator of the base number, and then we apply the positive exponent. Examples: 49 = 7 3 = 343. 81 = 3 5 = 243. = 4 = . 216 = (6) 3 = 6 3 3 = 216(6) = 1296.