Final answer:
The question concerns using properties of logarithms and exponential numbers in mathematics, specifically with base 10, allowing for the multiplication and subtraction of numbers in exponential form without a calculator.
Step-by-step explanation:
The student is asking about exponential functions and logarithms, specifically dealing with the properties of the common logarithm (base 10) and exponential numbers. When working with powers of 10 and logarithms, one can use the properties of exponents and logarithms to simplify expressions without a calculator. For instance, if given the task to multiply (4.506 x 104) by (1.003 x 102), you should first multiply the coefficient (4.506 by 1.003) and then add the exponents of the powers of 10 (4 + 2), resulting in a new power of 10.
Similarly, when subtracting exponential numbers, you convert them to the same power of 10, subtract the digit terms, and if necessary, adjust the exponential term. This understanding allows the student to solve problems involving exponential notation, including evaluating expressions without a calculator by using the rules of exponents and logarithms.