How to Rewrite Radicals Into Exponents

You can rewrite radicals as fractional exponents.

To rewrite a radical as an exponent you must first understand the relationship between the two mathematical expressions. The n-th root of a number is equal to that number to the 1/n power. For example, the 4th root of 16 is equal to 16 to the 1/4 power.

Instructions

1. Determine the number in front of the radical sign. This is the value, n, that will be translated into the power of the exponent. A radical with no preceding number indicates a square root, and the n value should be assumed to be 2.

2. Take the number under the radical sign and write it with the exponent 1/n. For example, if the number under the radical is 8 and the number found in Step 1 is 3, then rewrite the radical as 8 to the 1/3 power.

3. Check your work by solving both equations. If the calculations cannot be done by hand, use a calculator. Using the example above, the 3rd root of 8 is 2, and 8 to the 1/3 power is also 2.

References

• Purplemath: Fractional (Rational) Exponents
• Interactive Mathematics: Fractional Exponents