Math Problem Statement

6.14 x 10^4 ÷ (5.60 x 10^-2 x 2.408 x 10^9) can be written in the form b × 10^n. Write b correct to 2 decimal places and n as an integer.

Solution

The expression shown in your image, (5.60×1012×2.408×1010)(5.60 \times 10^{-12} \times 2.408 \times 10^{10}), can be rewritten in scientific notation in the form b×10nb \times 10^n. Let's compute this:

First, we multiply the coefficients: 5.60×2.4085.60 \times 2.408

Then, we add the exponents of 10: 12+10-12 + 10

Let's calculate the resulting values for bb and nn.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Exponents
Multiplication and Division of Powers of Ten

Formulas

Multiplication of powers of 10: (a x 10^m) x (b x 10^n) = (a x b) x 10^(m+n)
Division of powers of 10: (a x 10^m) ÷ (b x 10^n) = (a ÷ b) x 10^(m-n)

Theorems

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Suitable Grade Level

Grades 9-12