QuestionAugust 24, 2025

Perform the indicated computation . Write the answer in scientific notation. (15times 10^5)/(3times 10^-2) 5times 10^7 10times 10^7 10times 10^3 5times 10^3

Perform the indicated computation . Write the answer in scientific notation. (15times 10^5)/(3times 10^-2) 5times 10^7 10times 10^7 10times 10^3 5times 10^3
Perform the indicated computation . Write the
answer in scientific notation.
(15times 10^5)/(3times 10^-2)
5times 10^7
10times 10^7
10times 10^3
5times 10^3

Solution
4.2(273 votes)

Answer

2.5 \times 10^{21} Explanation 1. Simplify the division Divide 15 \times 10^5 by 3 \times 10^{-2} using \frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n}. \frac{15}{3} \times 10^{5 - (-2)} = 5 \times 10^{7}. 2. Multiply with remaining terms Multiply 5 \times 10^{7}, 10 \times 10^{7}, 10 \times 10^{3}, and 5 \times 10^{3}. (5 \times 10^{7}) \times (10 \times 10^{7}) \times (10 \times 10^{3}) \times (5 \times 10^{3}) = 5 \times 10^{7} \times 10 \times 10^{7} \times 10 \times 10^{3} \times 5 \times 10^{3}. 3. Combine powers of ten Combine powers: 5 \times 10^{7} \times 10^{7} \times 10^{3} \times 10^{3} = 5 \times 5 \times 10^{7+7+3+3}. 4. Calculate final result 25 \times 10^{20}. 5. Convert to scientific notation Scientific notation: 2.5 \times 10^{21}.

Explanation

1. Simplify the division<br /> Divide $15 \times 10^5$ by $3 \times 10^{-2}$ using $\frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n}$.<br /> $\frac{15}{3} \times 10^{5 - (-2)} = 5 \times 10^{7}$.<br /><br />2. Multiply with remaining terms<br /> Multiply $5 \times 10^{7}$, $10 \times 10^{7}$, $10 \times 10^{3}$, and $5 \times 10^{3}$.<br /> $(5 \times 10^{7}) \times (10 \times 10^{7}) \times (10 \times 10^{3}) \times (5 \times 10^{3}) = 5 \times 10^{7} \times 10 \times 10^{7} \times 10 \times 10^{3} \times 5 \times 10^{3}$.<br /><br />3. Combine powers of ten<br /> Combine powers: $5 \times 10^{7} \times 10^{7} \times 10^{3} \times 10^{3} = 5 \times 5 \times 10^{7+7+3+3}$.<br /><br />4. Calculate final result<br /> $25 \times 10^{20}$.<br /><br />5. Convert to scientific notation<br /> Scientific notation: $2.5 \times 10^{21}$.
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