Final answer:
Expressions using properties of exponents are simplified by applying exponent rules, such as adding exponents when multiplying terms with the same base. Scientific notation is used for very large or small numbers, expressing them as a product of a number between 1 and 10 and a power of 10.
Step-by-step explanation:
The question is asking to simplify expressions using the properties of exponents. For example:
- a. 44 - 42: When we subtract two numbers with the same base, we work on each term independently since exponent properties don't have any rule for subtraction.
- b. 74 x 78: We can use the property of exponents which states that when multiplying two terms with the same base, we can add the exponents. Therefore, 74+8 or 712 is the simplified expression.
We will also cover the scientific notation which makes it simpler to handle very large or small numbers. It is written as a product of a number between 1 and 10 and a power of 10. Converting to scientific notation involves moving the decimal point to create a new number from 1 up to 10 and then count the number of places the decimal has moved to determine the exponent on the 10.
Example:
a. (4.6 × 10-5) × (2.09 × 103) = 9.614 × 10-2
Notice that when you multiply two numbers in scientific notation, you multiply the base numbers and add the exponents.