By algebraic handling, the simplified radical form of [tex]\sqrt[5]{96 \cdot t^{15}\cdot u^{17}}[/tex] is [tex]2 \cdot \sqrt[5]{3}\cdot t^{3}\cdot u^{17 / 5}[/tex].
How to simplify a radical expression
In this problem we have a radical expression that must be simplified solely by algebraic properties. The complete procedure is shown below:
- [tex]\sqrt[5]{96 \cdot t^{15}\cdot u^{17}}[/tex] Given
- [tex]\sqrt[5]{(2^{5}\cdot 3) \cdot t^{15}\cdot (u^{15}\cdot u^{2})}[/tex] Associative and commutative properties / Multiplication of powers of equal base / Factor decomposition
- [tex]2 \cdot \sqrt[5]{3} \cdot t^{3} \cdot u^{3}\cdot u^{2/5}[/tex] Product of quintic roots / Definition of quintic root / Power of a power / Quintic root of a product
- [tex]2 \cdot \sqrt[5]{3}\cdot t^{3}\cdot u^{17 / 5}[/tex] Multiplication of powers of equal base
- [tex]2 \cdot \sqrt[5]{3\cdot u^{17}} \cdot t^{3}[/tex] Product of quintic roots / Definition of quintic root / Power of a power / Quintic root of a product / Result
Therefore, by algebraic handling, the simplified radical form of [tex]\sqrt[5]{96 \cdot t^{15}\cdot u^{17}}[/tex] is [tex]2 \cdot \sqrt[5]{3}\cdot t^{3}\cdot u^{17 / 5}[/tex].
To learn more on radical equations: https://brainly.com/question/8606917
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