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Chapter 0: Problem 93

Factor and simplify each algebraic expression. $$x^{\frac{3}{2}}-x^{\frac{1}{2}}$$

Short Answer

Expert verified
The factorized and simplified form of the expression \(x^{\frac{3}{2}}-x^{\frac{1}{2}}\) is \(x^{\frac{3}{2}}\).

Step by step solution

01

Identification of the common factor

The given expression is \(x^{\frac{3}{2}}-x^{\frac{1}{2}}\). Here \(x^{\frac{1}{2}}\) is the common factor in both terms.
02

Factorization of the expression

Keeping \(x^{\frac{1}{2}}\) as common factor from each term, we get \(x^{\frac{1}{2}}(x^{\frac{3}{2} - 1})\). This reduces to \(x^{\frac{1}{2}}(x) = x^{\frac{1}{2}}x\).
03

Simplification of the expression

When we multiply \(x^{\frac{1}{2}}\) and \(x\), the powers add up as per the rules of power math: \(a^m 脳 a^n = a^{m+n}\). So it becomes \(x^{\frac{3}{2}}\).

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