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The cube root of a number is the value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2, because 2 x 2 x 2 = 8.
In mathematical terms, the cube root of a number 'a' is written as \(\root{3}{a}\).
This notation is used to show that we are looking for the number that provides 'a' when taken to the third power.
In our specific example, we are dealing with \(\root{3}{20}\). This calls for finding the value that, when raised to the power of 3, equals 20.
Since 20 is not a perfect cube (like 8 or 27), the cube root of 20 does not yield a whole number. Instead, it is an approximation.
This leads us to understanding the use of fractional exponents, which can simplify working with roots, as well as expressing them in exponential form.

A radical expression involves roots, such as square roots and cube roots. The radical symbol (\(\sqrt{}\)) is used to denote these types of expressions.
Certainly, you have worked with square roots before, where \(\sqrt{a}\) denotes the square root of 'a'.
In a similar manner, \(\root{n}{a}\) represents the n-th root of 'a'.
For cube roots, we specifically use the form \(\root{3}{a}\). Simplifying and expressing these radicals can make it easier to handle them in various mathematical contexts.
In the given exercise, \(\sqrt[3]{20}\) is a radical expression, explicitly referring to the cube root of 20.
Understanding how to convert radical expressions allows for more versatile application in algebra and simplifying complex expressions into exponential notation.

Fractional exponents provide an efficient way to express roots using exponents.
To convert a radical expression to exponential form, remember that \(\root{n}{a}\) is equivalent to \(a^{1/n}\). For instance, a square root, \(\sqrt{a}\), can be written as \(a^{1/2}\).
In our example, the cube root \(\sqrt[3]{20}\) converts to \(20^{1/3}\), because the fractional exponent \(1/3\) indicates a division of the exponent by 3.
This equivalency is extremely useful in algebra, as it often simplifies multiplication and division of roots.
For instance, multiplying \(20^{1/3}\) by \(20^{2/3}\) becomes easier, as it simplifies to \(20^{(1/3 + 2/3)} = 20^1 = 20\).
Therefore, understanding fractional exponents leads to easier manipulation and simplification of expressions that involve roots.