ISEE Word Problems Question 164: Answer and Explanation

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Question: 164

11. If x and y are both integers, what is (8.0 × 10^x)(6.0 × 10^y) expressed in scientific notation?

A. 48.0 × 10^xy
B. 4.8 × 10^x ⁺ ^y ^{+ 1}
C. 4.8 × 10^x ⁺ ^y
D. 4.8 × 10^xy

Correct Answer: B

Explanation:

The answer is B

With like bases, add the exponents when the terms are multiplied. (10^x)(10^y) = 10^{x + y}. The product of the two numerical terms, 8.0 and 6.0 equals 48. However, 48 must be expressed as 4.8 × 10¹ in scientific notation. Because this requires multiplying the exponents again, add the 1 to the exponent: 10^x ⁺ ^y ^{+ 1}.

You can plug in values for x and y. If x and y are both set to 2, you have 800 × 600 = 480,000. Choice (B) matches.

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