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Chapter 0: Problem 94

Factor and simplify each algebraic expression. $$x^{\frac{3}{4}}-x^{\frac{1}{4}}$$

Short Answer

Expert verified
The factorized and simplified form of \(x^{\frac{3}{4}}-x^{\frac{1}{4}}\) is \(x^{\frac{1}{4}}(x^{\frac{1}{2}} - 1)\).

Step by step solution

01

Factorize the Expression

For the expression \(x^{\frac{3}{4}}-x^{\frac{1}{4}}\), we focus on what is common between both terms which is \(x^{\frac{1}{4}}\). So, we factor out \(x^{\frac{1}{4}}\) from both terms: \(x^{\frac{1}{4}}(x^{\frac{3}{4}}/x^{\frac{1}{4}} - x^{\frac{1}{4}}/x^{\frac{1}{4}})\).
02

Simplify the Expression

In this step, we simplify the factored expression. We'll use the following law: \(x^{a}/x^{b} = x^{a-b}\). So, the expression simplifies to: \(x^{\frac{1}{4}}(x^{\frac{3}{4}} - \frac{1}{4}} - 1)\) which simplifies further to \(x^{\frac{1}{4}}(x^{\frac{1}{2}} - 1)\).
03

Re-write in Simplest Form

Evaluate into simple forms if possible. The expression can't be simplified anymore, so the simplest form is \(x^{\frac{1}{4}}(x^{\frac{1}{2}} - 1)\).

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Most popular questions from this chapter

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$$\text { Solve for } C: \quad V=C-\frac{C-S}{L} N$$.
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