Q: If the coefficient of the expression ax is in fraction and the exponent is positive the expression will be a polynomial?

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Not necessarily. Every exponent in the exponent must be a non-negative integer. This is not what you have specified. For example, if n = 3.5, it is not a term in a polynomial expression.

A polynomial.

(2a3)(10a5)/4a1

Example: (4x)-2 The answer to this would be 1/ 16x2. Multiply it out as if the negative exponent was not there ((4x)2), then that will be the denominator of the fraction. The numerator is one.

It means that it is an exponent, and that it is not a rational number - i.e., one that can be written as a fraction of two integers.

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Not necessarily. Every exponent in the exponent must be a non-negative integer. This is not what you have specified. For example, if n = 3.5, it is not a term in a polynomial expression.

Just write ANY fraction, with a polynomial in the numerator, and a polynomial in the denominator.

A numerical or constant quantity placed before and multiplying the variable in an algebraic expression

(Any proper fraction)2 has a value less than 1 .

A polynomial.

Flip the fraction top-to-bottom, and delete the minus sign from the exponent.

No. A polynomial is two or more numbers connected with plus or minus signs.A fraction is just a single number.I guess you could call a fraction a "monomial" if you want to, but definitely nota "polynomial".

Yes.

I am not entirely sure what your expression looks like. If the "x" appears in the denominator, as in 7/x, then it is NOT a polynomial. Polynomials only have powers of the variables involved that are positive integers.

The reciprocal of a^(-x/y) is 1/a^(x/y). The fact that the exponent is a fraction makes no difference.

Why not? An exponent is just like any other number.

A fraction