Math Problem Statement

Calculate (3 × 10^(-6)) × (3 × 10^(-13)). Give your answer in standard form.

Solution

The expression to calculate is:

(3×106)×(3×1013)(3 \times 10^{-6}) \times (3 \times 10^{-13})

To simplify this:

  1. Multiply the constants: 3×3=93 \times 3 = 9

  2. Add the exponents of 10 (using the property of exponents 10a×10b=10a+b10^a \times 10^b = 10^{a+b}): 6+(13)=19-6 + (-13) = -19

Therefore, the expression becomes:

9×10199 \times 10^{-19}

In standard form, the answer is:

9×10199 \times 10^{-19}

Would you like further details or have any questions?

Here are some related questions:

  1. How do you multiply numbers in scientific notation?
  2. What are the rules for adding exponents?
  3. What is standard form in mathematics?
  4. How do you handle negative exponents?
  5. How can you simplify expressions with powers of 10?

Tip: When multiplying numbers in scientific notation, remember to multiply the coefficients and add the exponents.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Scientific Notation
Exponent Rules
Multiplication

Formulas

Multiplication of coefficients: a × b
Addition of exponents: 10^a × 10^b = 10^(a + b)

Theorems

Exponent Rules

Suitable Grade Level

Grades 8-10