Final answer:
To write the cube root as a fraction, express it as a power with an exponent of 1/3, such as x^(1/3) for the cube root of x. This representation is based on the rules of exponents where fractional exponents indicate roots.
Step-by-step explanation:
The cube root can be written as a fraction with an exponent of 1/3. For example, the cube root of x (written as √x) can be expressed as x^(1/3).The concept of cube roots as fractional exponents stems from the rules of exponents. Raising a number to the power of 1/3 is equivalent to taking its cube root, similar to how squaring a number (e.g., 5^2) and then taking the square root results in the original number. Multiplying exponents when the same base is raised to different powers and the reverse process, which is rooting (finding square roots, cube roots, etc.), can be translated into expressions with fractional exponents.
For instance, (3^(1.7)) is the equivalent of taking the 10th root of 3 raised to the 17th power. The use of fractional exponents is particularly helpful when solving equations involving roots or when calculating volume, where the exponent defines the dimensionality of the cube.To write the cube root as a fraction, we can use the exponent property that states that the cube root of a number can be represented as a fraction with a numerator of 1 and a denominator equal to the cube of the number. For example, the cube root of 8 can be written as 1/83. This can be simplified to 1/512.