Question

Change exponential expression to radical expression

Answer 1

1. The radical expression is
`\( \sqrt[1]{125^2} \).`

2. The radical expression is
`\( √(5x) \).`

3. The radical expression is
`\( \sqrt[4]{16^3} \).`

4. The radical expression is
`\( \sqrt[5]{xy^2} \).`

5. The radical expression is
`\( \sqrt[5]{5^1 * 5^2} \).`

To change exponential expressions to radical expressions, you use the fact that
`\(\sqrt[b]{a^c} = a^(c/b)\)`. Here are the conversions for the given expressions:

1.
`\( (125)^{(2)/(1)} \)` is the same as
`\( \sqrt[1]{125^2} \).`

So, the radical expression is
`\( \sqrt[1]{125^2} \).`

2.
`\( 5x^{(1)/(2)} \)` is the same as
`\( \sqrt[2]{5x^1} \).`

So, the radical expression is
`\( √(5x) \).`

3.
`\( 16^{(3)/(2) * (3)/(4)} \)` is the same as
`\( \sqrt[4]{16^3} \)`.

So, the radical expression is
`\( \sqrt[4]{16^3} \).`

4.
`\( xy^{(2)/(5)} \)` is the same as
`\( \sqrt[5]{xy^2} \).`

So, the radical expression is
`\( \sqrt[5]{xy^2} \).`

5.
`\( 5^{(1)/(5)} * 5^{(2)/(5)} \)`is the same as
`\( \sqrt[5]{5^1 * 5^2} \).`

So, the radical expression is
`\( \sqrt[5]{5^1 * 5^2} \).`