Final answer:
Decimal exponents like 3¹.7 are calculated with a calculator using the '^' or a dedicated exponent button, and writing down these calculations helps to understand. The TI-83 series calculators can perform statistical tests like ZInterval, and scientific notation is used to represent large or small numbers.
Step-by-step explanation:
When we are given a number like 3¹.7 we encounter something beyond integer powers, which presents a problem when we can't simply write out the multiplication as with 34 equals 3· 3· 3· 3. However, decimal exponents like 3¹.7 are well-defined mathematically and calculators can handle these calculations without difficulty. When entering these into a calculator, you will often use the ^ button or some calculators have a dedicated button for this type of exponentiation.
To better understand and accurately compute the power of a number that is not an integer, it is recommended to write down these calculations on your notepad, as interacting with the numbers actively can improve comprehension. Calculators such as the TI-83, 83+, 84, and 84+ series can also assist with statistical calculations, as seen with ZInterval tests. For example, to conduct a ZInterval test on these models, you would follow a sequence of button presses that takes you through entering statistical data to reach your interval.
Mathematics involving large or small numbers can be easily handled using scientific notation, which expresses numbers in the form of a coefficient times a power of ten. This form is beneficial for simplifying the representation of very large or very small quantities and is essential in scientific fields. Drawing histograms and working with linear equations can also be facilitated by entering the data into a calculator, thus making these tools indispensable for students and professionals alike.