What to do with an exponent that is a fraction?
Fractional Exponents When the exponent is a fraction, you’re looking for a root of the base. The root corresponds to the denominator of the fraction. For example, take “125 raised to the 1/3 power,” or 125^1/3. The denominator of the fraction is 3, so you’re looking for the 3rd root (or cube root) of 125.
What is the rule for fractional exponents?
What is the Rule for Fractional Exponents? In the case of fractional exponents, the numerator is the power and the denominator is the root. This is the general rule of fractional exponents.
How do you rewrite a fractional exponent?
To rewrite a radical using a fractional exponent, the power to which the radicand is raised becomes the numerator and the root becomes the denominator….
| Example | ||
|---|---|---|
| Problem | Simplify. | |
| Rewrite the expression with the fractional exponent as a radical. | ||
| 6 • x2 | Find the square root of both the coefficient and the variable. | |
| Answer |
How do you solve fraction exponents?
To solve fractions with exponents, review the rules of exponents. You’ll distribute the exponent to the full fraction if indicated. Then, you’ll multiply the full fraction, the base, by itself the number of times directed by the exponent. Both exponents and fractions are important algebraic concepts.
What if the exponent is a fraction?
What is the fractional exponent rule?
What is the Rule for Fractional Exponents? In the case of fractional exponents, the numerator is the power and the denominator is the root. This is the general rule of fractional exponents. We can write xm/n as n√(xm).
How are fractional exponents like negative exponents?
Since we cannot take the even root of a negative number, we cannot take a negative number to a fractional power if the denominator of the exponent is even. A negative fractional exponent works just like an ordinary negative exponent.