Question

Write the following expression in simplified radical form. (See picture)

Answer 1

By algebraic handling, the simplified radical form of $\sqrt[5]{96 \cdot t^{15}\cdot u^{17}}$ is $2 \cdot \sqrt[5]{3}\cdot t^{3}\cdot u^{17 / 5}$.

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:

1. $\sqrt[5]{96 \cdot t^{15}\cdot u^{17}}$                    Given
2. $\sqrt[5]{(2^{5}\cdot 3) \cdot t^{15}\cdot (u^{15}\cdot u^{2})}$    Associative and commutative properties / Multiplication of powers of equal base / Factor decomposition
3. $2 \cdot \sqrt[5]{3} \cdot t^{3} \cdot u^{3}\cdot u^{2/5}$           Product of quintic roots / Definition of quintic root / Power of a power / Quintic root of a product
4. $2 \cdot \sqrt[5]{3}\cdot t^{3}\cdot u^{17 / 5}$                Multiplication of powers of equal base
5. $2 \cdot \sqrt[5]{3\cdot u^{17}} \cdot t^{3}$                  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 $\sqrt[5]{96 \cdot t^{15}\cdot u^{17}}$ is $2 \cdot \sqrt[5]{3}\cdot t^{3}\cdot u^{17 / 5}$.

To learn more on radical equations: brainly.com/question/8606917

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