Math Problem Statement

The query submitted by the user involves multiplication, division, and reciprocals involving powers of 10 notation from a math exercise sheet.

Solution

I see the image contains exercises related to multiplication, division, and reciprocals involving scientific notation and powers of 10. I can help solve some of these problems. Let's go through the exercises, starting with the ones you want to focus on.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Powers of 10
Multiplication and Division in Scientific Notation
Reciprocals

Formulas

Multiplication of powers of 10: (a × 10^n) × (b × 10^m) = (a × b) × 10^(n + m)
Division of powers of 10: (a × 10^n) ÷ (b × 10^m) = (a ÷ b) × 10^(n - m)
Reciprocal of 10^n = 1 / 10^n = 10^-n

Theorems

Laws of Exponents
Rules for Multiplication and Division of Exponents

Suitable Grade Level

Grades 9-10