Answer :
The simplest form is that form which can't be simplified further enough. For multivariable expressions, the simplest form is that form in which variables are as far and separated and clean to operate on as possible, along with that expression being simplified.
The expressions A, C and D are in their simplest form.
Given expressions are:
A: [tex]\dfrac{1}{3} + x^7[/tex]
B: [tex]x^{-9} - \dfrac{1}{y} \dfrac{1}{x^3} - \dfrac{1}{y^4}[/tex]
C: [tex]x^3 + \dfrac{1}{y} - t^6[/tex]
D: [tex]x^{-5} - y^{-4}[/tex]
How to check if the given expression is simplified?
Expression A: It is in the simplest form since any modification will make it more complex.
Expression B: It is not in the simplest form since many variables are still in the denominator and can be brought up in the numerators.
Expression C: It is in the simplest form since all the variables x, y and t are all separated, and any further modification will make them mingle in each other thus being more complex.
Expression D: It is in the simplest form since the variables are lying separately. Any further modification like for example fraction addition will make it more complex.
Thus, expression A, C and D are in their simplest form.
Learn more about simplification here:
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