Final answer:
The expression m² · m⁵ · m⁻³ simplifies to m⁴, by adding the exponents since they have the same base, resulting in option (a) m⁴.
Step-by-step explanation:
The expression m² · m⁵ · m⁻³ when simplified uses the rule that when you multiply powers with the same base, you add the exponents. In this case, the base is m and the exponents are 2, 5, and -3. To simplify, you would add the exponents: 2 + 5 + (-3) = 4. Therefore, the expression simplifies to m⁴, which corresponds to option (a) m⁴.
When powers of 10 are multiplied together, the powers are added together. For example, 10² × 10³ = 10²+3 = 10⁵. Similarly, in the expression we have (4.506 × 10⁴):× (1.003 × 10²), you would add the exponents of 10, which results in a power of 10⁶ when simplified.
Remember to always check that your result is in the correct scientific notation and has the correct significant figures.