# High School Math : Expressing Radicals as Exponents

## Example Questions

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### Example Question #1 : Expressing Radicals As Exponents

Convert the radical to exponential notation.

Explanation:

Remember that any term outside the radical will be in the denominator of the exponent.

Since does not have any roots, we are simply raising it to the one-fourth power.

### Example Question #1 : Radicals

What is the value of ?

2.41

3

9

27

243

243

Explanation:

An exponent written as a fraction can be rewritten using roots.   can be reqritten as .  The bottom number on the fraction becomes the root, and the top becomes the exponent you raise the number to. is the same as . This will give us the answer of 243.

### Example Question #3 : Expressing Radicals As Exponents

Express the following radical in rational (exponential) form:

Explanation:

To convert the radical to exponent form, begin by converting the integer:

Now, divide each exponent by  to clear the square root:

Finally, simplify the exponents:

### Example Question #4 : Expressing Radicals As Exponents

Express the following radical in rational (exponential) form:

Explanation:

To convert the radical to exponent form, begin by converting the integer:

Now, divide each exponent by  to cancel the radical:

Finally, simplify the exponents:

### Example Question #5 : Expressing Radicals As Exponents

Which fraction is equivalent to ?

Explanation:

Multiply the numerator and denominator by the compliment of the denominator:

Simplify the expression:

### Example Question #1 : Radicals

Simplify the following radical. Express in rational (exponential) form.

Explanation:

Multiply the numerator and denominator by the compliment of the denominator:

Simplify the expression:

### Example Question #7 : Expressing Radicals As Exponents

Choose the fraction equivalent to .

Explanation:

Multiply the numerator and denominator by the compliment of the denominator:

Simplify the expression:

### Example Question #1 : Expressing Radicals As Exponents

Simplify the following radical. Express in rational (exponential) form.

Explanation:

Multiply the numerator and denominator to the exponent:

Simplify the expression by combining like terms:

### Example Question #1 : Expressing Radicals As Exponents

Express the following radical in rational (exponential) form:

Explanation:

To convert the radical to exponent form, begin by converting the integer:

Now, divide each exponent by  to remove the radical:

Finally, simplify the exponents:

### Example Question #10 : Expressing Radicals As Exponents

Simplify:

Explanation:

Multiply the numerator and denominator to the exponent:

Simplify the expression by combining like terms:

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