35. Critique Reasoning Kristen was asked to write each of the numbers in the expression $$ 80,000 imes 25 $$ using exponents. Her response was $$ \left(8 imes 10^{3} ight) imes 5^{2} $$. Was Kristen's response correct? Explain.

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35. Critique Reasoning Kristen was asked to write each of the numbers in the expression $$ 80,000 	imes 25 $$ using exponents. Her response was $$ \left(8 	imes 10^{3}ight) 	imes 5^{2} $$. Was Kristen's response correct? Explain.

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The response is not correct. Here's why:

• The problem asked for each number in 80,000 × 25 to be rewritten using exponents.

• For 25, writing it as 5² is correct.

• However, 80,000 was written as 8 × 10³ by Kristen. Since 10³ = 1,000, this gives 8 × 1,000 = 8,000, which is not 80,000.

• In order to correctly represent 80,000, notice that 80,000 = 8 × 10⁴ (because 10⁴ = 10,000, and 8 × 10,000 = 80,000).

Thus, the correct exponent form for the expression should be (8 × 10⁴) × 5², not (8 × 10³) × 5².
Kristen's response was not correct. She wrote 80,000 as 8 × 10³, but 10³ equals 1,000, making 8 × 1,000 = 8,000, which is not 80,000. The correct exponent form for 80,000 is 8 × 10⁴. Therefore, the correct expression should be (8 × 10⁴) × 5².

35. Critique Reasoning Kristen was asked to write each of the numbers in the expression \( 80,000 \times 25 \) using exponents. Her response was \( \left(8 \times 10^{3}\right) \times 5^{2} \). Was Kristen's response correct? Explain.

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