Final answer:
The expression 7¹⁄² can be expressed in radical form as √7, which is the square root of 7. This reflects the principle where fractional exponents are equal to taking the root of the base number equivalent to the denominator of the fraction.
Step-by-step explanation:
The expression 7¹⁄² in radical form is written as the square root of 7, which can be expressed as √7. This comes from the property that fractional exponents indicate roots, specifically that the denominator of the fraction is the index of the root. Therefore, an exponent of ¹⁄² is equivalent to the square root. The equivalent radical expression for 7¹⁄² is √7.
When dealing with fractional exponents, it's important to remember that the numerator of the fraction can also represent the power to which you raise the number after taking the root if it is more than 1. However, in this case, the numerator is 1, which means we only take the square root without further raising it to any power.
Radical and fractional exponent notation are interchangeable, with the radical sign being the more traditional and visual method. Fractional exponents tend to be more concise especially when dealing with more complex algebraic expressions.