In calculus it is frequently important to write aņexpression in the form \( c x^{n} \), where \( c \) is a constant and \( n \) is a rational number, Write the following expression in this form,
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The Deep Dive
To express the given function in the form \( c x^{n} \), simply identify and isolate the constant and power of \( x \). For example, if you have the expression \( 5x^2 \), it is already in the desired form with \( c = 5 \) and \( n = 2 \). However, if the expression is something like \( \frac{3}{x} \), you can rewrite it as \( 3x^{-1} \), setting \( c = 3 \) and \( n = -1 \). Understanding how to manipulate expressions in this way is not only critical for mastering calculus but also helps in simplifying integration and differentiation processes. Keep practicing with different expressions to become comfortable with this transformation!