Final answer:
To simplify powers of ten expressions, you add exponents when multiplying and subtracting exponents when dividing the powers of ten. For instance, (8.552 × 10^6) ÷ (3.129 × 10^3) simplifies to approximately 2.731 × 10^3. For whole number powers like 5^2 and 5^3 - 10^2, calculate each power and then perform the arithmetic operation.
Step-by-step explanation:
To simplify the power of ten expressions, there are specific rules to follow:
- When multiplying powers of ten, you add the exponents.
- When dividing powers of ten, you subtract the exponent of the denominator from the exponent of the numerator.
For example, if we want to simplify (8.552 × 106) ÷ (3.129 × 103), we divide the coefficients (8.552/3.129) and subtract the exponents (6-3), resulting in approximately 2.731 × 103, assuming you'd simplify the division of coefficients without a calculator.
To simplify expressions such as 52 B) 53 - 102, you need to calculate each power independently and then perform the subtraction:
- 52 = 25
- 53 - 102 = 125 - 100 = 25