Astronomy Practice Exam

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What does the rule of multiplication for powers of ten state?

10^A / 10^B = 10^(B-A)
10^A x 10^B = 10^(A+B)
10^A + 10^B = 10^(A+B)
10^A - 10^B = 10^(A-B)

The correct answer is: 10^A x 10^B = 10^(A+B)

The rule of multiplication for powers of ten states that when you multiply two powers of ten, you add their exponents. Thus, for any two numbers A and B, the expression 10 raised to the power of A multiplied by 10 raised to the power of B is equal to 10 raised to the power of the sum of A and B. This can be expressed mathematically as 10^A × 10^B = 10^(A + B). This principle comes from the laws of exponents, which dictate that when you multiply numbers with the same base (in this case, the base 10), you simply add the exponents. This rule is fundamental in scientific notation and helps simplify calculations involving large or small numbers. The other options represent different mathematical operations that do not accurately describe the multiplication of powers of ten. For example, division yields a subtraction of exponents, while addition or subtraction of exponential terms does not follow the same rules and produces different outcomes.