Math Problem Statement

Multiply. Write your answer in scientific notation: (2 × 10^-1)(2 × 10^-6)

Solution

We are tasked with multiplying the two expressions in scientific notation:

(2×101)(2×106)(2 \times 10^{-1})(2 \times 10^{-6})

Step-by-Step Solution:

  1. Multiply the constants: 2×2=42 \times 2 = 4

  2. Multiply the powers of 10: 101×106=101+(6)=10710^{-1} \times 10^{-6} = 10^{-1 + (-6)} = 10^{-7}

  3. Combine the results: 4×1074 \times 10^{-7}

Thus, the product in scientific notation is:

4×1074 \times 10^{-7}

Would you like more details or have any questions?

Related Questions:

  1. How do you add or subtract numbers in scientific notation?
  2. What are the rules for dividing numbers in scientific notation?
  3. How would you convert 4×1074 \times 10^{-7} to decimal notation?
  4. What is the general rule for multiplying exponents with the same base?
  5. How do you handle negative exponents in calculations?

Tip:

When multiplying in scientific notation, remember to handle the coefficients and powers of 10 separately.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Exponent Rules

Formulas

Multiplication of numbers in scientific notation: (a × 10^m)(b × 10^n) = (a × b) × 10^(m+n)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 6-8