Final answer:
Moe's answer is incorrect because 10^3 equals 1,000, not 30. The correct method involves multiplying the number 10 by itself three times. Understanding exponents and scientific notation is key in solving such problems correctly.
Step-by-step explanation:
No, Moe's answer of 10^3 = 30 is incorrect. The correct way to solve 10^3 is to recognize it as 10 multiplied by itself three times. Thus, 10^3 is actually 10 x 10 x 10, which equals 1,000. To understand how to work with exponents, especially in scientific notation, it's essential to grasp that when powers of 10 are multiplied, you add the exponents, and when a single number like 10 is raised to an exponent, you 'multiply' the base (10) that number of times.
As an example in scientific notation, the product of (4.506 × 10^4) and (1.003 × 10^2) can be solved by multiplying the non-exponent numbers (4.506 and 1.003) and then adding the exponents of 10 (4 and 2). The operation (4.506 × 1.003) × 10^(4+2) would give us the result without converting to scientific notation. The concept also applies to simpler operations such as 3.2 × 10^3 × 2 × 10^2 which equals 6.4 × 10^5.
Memorizing the operation of exponents can be beneficial, but understanding the concept that 10^3 is 10 × 10 × 10, and so on, can be more intuitive and help with solving exponentiation problems. Scientific notation simplifies the arithmetic operations involving exponents and powers of ten, and understanding how to manipulate these scientific notations is crucial in mathematics