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Chapter 7: Problem 7

Which of the following is equivalent to \(x^{\frac{3}{2}}\) ? C \(\sqrt{x^3}\) \(\frac{3}{2} x\) \(\frac{x^2}{x^2}\) I don't know.

Short Answer

Expert verified
The equivalent expression to \(x^{\frac{3}{2}}\) is C: \(\sqrt{x^3}\).

Step by step solution

01

Understanding the given expression

The given expression is \(x^{\frac{3}{2}}\). In exponential expressions, when the exponent is a fraction, the numerator represents the power to which the base number is raised, and the denominator represents the root. Thus, this expression can be rewritten as \(\sqrt{x^3}\), where 3 is the power (numerator) and the square root is the root (denominator).
02

Evaluate the choices

Looking at the available options, C \(\sqrt{x^3}\) represents the cube of x under the square root, which is the equivalent expression for \(x^{\frac{3}{2}}\). Thus, choice C is the correct answer. The other options do not correctly express the power and root operations implied by the given expression.

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Most popular questions from this chapter

Line 1 is defined by \(y=3 x+7\), and line 2 is parallel to line 1 . What is the slope of line 2 ? O \(-3\) 03 O \(\frac{1}{3}\) I don't know.

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