The example below shows one method to simplify a radical expression by rewriting each root as an exponential expression and using the rules of exponents to simplify to an expression with one base and its exponent.
\(\sqrt x \cdot \sqrt {x^3} = x^{\frac12}\cdot x ^{\frac32}\), then \(x^{\frac12}\cdot x^{\frac32}=x^{\frac42}=x^2\)
Match each expression on the left to its simplified version on the right.
| 1. \(\sqrt[3]{x^2}\cdot \sqrt[3]{x^2}\) | a. \(x^3\) |
| 2. \(2\sqrt{x^3}\cdot\sqrt{x^5}\) | b. \(2x^2\) |
| 3. \(\sqrt x \cdot \sqrt[3]x\) | c. \(2x^4\) |
| 4. \((\sqrt{x^3})^2\) | d. \(x^{\frac56}\) |
| 5. \(\sqrt{2x^3}\cdot\sqrt{2x}\) | e. \(x^{\frac43}\) |
Answers : 1-e, 2-c, 3-d, 4-a, 5-b