Which of the following expressions is equivalent to: 1200 X (5 X 10⁷)?

Rationale

6.0 × 10¹⁰ is equivalent to 1200 X (5 X 10⁷).

To simplify the expression 1200 X (5 X 10⁷), we first multiply 1200 by 5 to obtain 6000, and then express 6000 as 6.0 X 10³. Multiplying this by 10⁷ gives us 6.0 X 10¹⁰, confirming that choice B is correct.

A (12X10¹⁰) YOUR ANSWER

This option suggests that the result of the multiplication is 12. However, when calculating, 1200 multiplied by 5 results in 6000, which is not equivalent to 12 X 10¹⁰. This choice misrepresents the multiplication by incorrectly scaling the coefficient.

B (6.0 × 10¹⁰) CORRECT

This is the correct expression obtained by simplifying the original equation. By multiplying 1200 and 5, we arrive at 6000, which can be expressed as 6.0 X 10³, and when combined with 10⁷ yields 6.0 X 10¹⁰.

C (6.0X10¹¹) YOUR ANSWER

This choice incorrectly increases the exponent to 11, which would imply that 6000 is multiplied by an additional factor of 10. The calculation shows that we only need to add the exponents of 10³ and 10⁷, leading to a total of 10¹⁰ instead.

D (7.2X10¹³) YOUR ANSWER

This expression suggests a much larger result than what is calculated. The multiplication of 1200 and 5 does not support reaching an exponent of 13, indicating a significant miscalculation in both the coefficient and exponent.

E (9.4X10¹⁴) YOUR ANSWER

This option also provides an incorrect magnitude and exponent. The calculations yield far less than what this expression suggests, indicating a misunderstanding of the multiplication and exponential rules.

Conclusion

Upon evaluating the original expression, 1200 X (5 X 10⁷) simplifies correctly to 6.0 X 10¹⁰, demonstrating proper multiplication and exponent rules. The other options misrepresent the calculations either by incorrect coefficients or exponents, reaffirming that choice B accurately reflects the result of the expression.