Final answer:
Exponents, both integral and fractional, may result in rational or irrational numbers depending on the base and exponent involved. Exponential arithmetic involves multiplying, dividing, and raising powers, each with its own set of rules. (Option B).
Step-by-step explanation:
When dealing with exponents, whether they are integral or fractional, the results can vary widely depending on the base and the exponent. For example, raising an integer to a positive integral power typically results in another integer, while using fractional exponents (which represent roots) can yield rational or irrational numbers.
Negative exponents indicate division and result in fractions or decimals, meaning their outcomes depend on the value of the base raised to the negative exponent.
It's important to understand the rules of exponential arithmetic. When raising a power to another power, you multiply exponents.
When multiplying two exponentials with the same base, you add the exponents together. When dividing exponentials with the same base, you subtract the exponents. When dealing with scientific notation, for instance, multiplying two numbers will have you adding the exponents of the power of 10, and dividing them would involve subtracting the exponents.
Therefore, integral and fractional exponents: (Option B).
- May result in rational or irrational numbers