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Part 1
What is the value of n? Use pencil and paper. Explain why the exponent on the left side of the equation is not equal to the sum of the exponents on the right side.
3.5 times 10 Superscript 10equalsleft parenthesis 5 times 10 Superscript 5 right parenthesis left parenthesis 7 times 10 Superscript n right parenthesis
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Part 1
The value of n is
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GPT-5 mini
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n = 4
Work: (5 × 10^5)(7 × 10^n) = 35 × 10^{5+n} = 3.5 × 10^{6+n}.
So 3.5 × 10^{10} = 3.5 × 10^{6+n} ⇒ 10 = 6 + n ⇒ n = 4.
Explanation: You cannot just add the exponents 5 and n to get 10 because the numeric coefficients (5 and 7) multiply to 35, which is 3.5 × 10^1 and thus increases the power of 10 by 1 when put into proper scientific notation.
Work: (5 × 10^5)(7 × 10^n) = 35 × 10^{5+n} = 3.5 × 10^{6+n}.
So 3.5 × 10^{10} = 3.5 × 10^{6+n} ⇒ 10 = 6 + n ⇒ n = 4.
Explanation: You cannot just add the exponents 5 and n to get 10 because the numeric coefficients (5 and 7) multiply to 35, which is 3.5 × 10^1 and thus increases the power of 10 by 1 when put into proper scientific notation.
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