if you have a problem where you are multiplying numbers with exponents (both positive and negative) and your answer ends up with a negative exponent what is the reason you make a fraction out of it and put it on the bottom as a positive?

why cant you have a negative exponent in an answer?

You are right. You can write the answer either way.

For example, if a and b are both positive,
x^a*x^-b = x^(a-b) or 1/x^(b-a)

but why cant there be a neg. on top? why do u move it to the bottom and make it positive?(note:,5,2 and 4 are exponents)

(4a-6b5)(7a2b4)= 28a-5b9
the final answer will be 28b9
over
a5
my question was why do you move the "a" negative 5 to the bottom and make it a postive "a" 5
I hope i'm wording this right.

You can. Just move the exponent up or down between numerator and denominator and change the sign. It's the same number either way.

When you encounter a situation where you have a product of numbers with exponents, including both positive and negative exponents, and your answer ends up with a negative exponent, the reason you convert it into a fraction is to maintain consistency and adhere to the rules of exponentiation.

In mathematics, negative exponents indicate reciprocals or fractions. To understand why you make a fraction out of it and place it on the bottom as a positive exponent, let's consider an example:

Suppose you have the expression 2³ * 2⁻⁵. According to the rules of exponentiation, when you multiply two numbers with the same base and different exponents, you add their exponents. So, in this case, you would get 2³⁺⁻⁵ = 2⁻².

The exponent 2⁻² signifies that the base 2 is in the denominator, meaning it is a fraction. In other words, 2⁻² is the reciprocal of 2². To avoid negative exponents, you can create a fraction by placing the term with the negative exponent in the denominator with a positive exponent: 1 / 2².

In general, negative exponents denote division or fractions. So, when you have an answer with a negative exponent, you can convert it into a fraction by placing the term with the negative exponent in the denominator with a positive exponent.

It's important to note that working with positive exponents makes it easier to handle calculations and express results in a standard mathematical form. Negative exponents are not typically preferred because they introduce fractions into the equation, which can complicate further calculations.