Simplifying whole numbers with fraction exponents involves understanding how to interpret the exponents and then applying the basic rules of exponents. A fraction exponent indicates both a root and a power. For example, a whole number raised to a fraction as an exponent, like am/n, means you take the nth root of a and then raise the result to the mth power.
Here’s how to simplify it step-by-step:
- Identify the whole number and the fraction exponent: Let’s say you have the number 8 and the exponent 2/3, which can be written as 82/3.
- Break down the fractional exponent: The number 2/3 tells you to first find the cube root (because of the 3 in the denominator), and then square the result (because of the 2 in the numerator).
- Calculate the cube root: The cube root of 8 is 2, since 2 x 2 x 2 = 8.
- Square the result: Now, take the result (which is 2) and square it: 2 x 2 = 4.
Therefore, 82/3 = 4.
In summary, when simplifying whole numbers with fraction exponents, remember to break down the exponent into its root and power components, perform the root calculation first, then raise the result to the power specified by the numerator.