Simplify the following expression: [tex]x^7-\frac{27 x^4}{x^3}[/tex]
Answer (1)
x 7 − 27 x
Explanation
Understanding the Problem We are given the expression x 7 − x 3 27 x 4 and we want to simplify it.
Simplifying the Fraction First, we simplify the fraction x 3 27 x 4 . Since x 4 = x 3 ⋅ x , we have x 3 27 x 4 = x 3 27 ⋅ x 3 ⋅ x = 27 x .
Substituting Back Now, we substitute this back into the original expression: x 7 − x 3 27 x 4 = x 7 − 27 x .
Final Expression Thus, the simplified expression is x 7 − 27 x .
Examples
In physics, this kind of simplification can be useful when modeling forces or energies that depend on position. For example, if you have a potential energy function that looks like x 7 − x 3 27 x 4 , simplifying it to x 7 − 27 x can make it easier to analyze the motion of an object under that potential. This simplification allows for easier calculation of forces and other relevant physical quantities.
