Rational Exponents – Writing Radicals in Exponential Form

Writing Radicals in Exponential Form

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The problems in this lesson involve writing radicals in exponential form. To write radicals as exponents, the root of the radical becomes the denominator of the fraction in the exponent, and the power on the radical becomes the numberator of the fraction on the exponent. For example, to simplify the 11th root of 2 to the 13th power, we first convert the 11th root of 2 to 2^(1/11), so we have [2^(1/11)]^13. Next, since we have a power taken to another power, we multiply the exponents to get 2^(11/13). It's important to understand how to write any radical as an exponent, not just a square root as an exponent or a cube root as an exponent.
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