The image presents two math problems: Problem 4: Simplify the expression $\frac{3 \times 10^2}{5 \times 10^4}$ and express the answer in standard form. Problem 5: Divide $\frac{1.2 \times 10^7}{4 \times 10^3}$ and express the result in standard form.

1. Problem Description

The image presents two math problems:

Problem 4: Simplify the expression $\frac{3 \times 10^2}{5 \times 10^4}$ and express the answer in standard form.

Problem 5: Divide $\frac{1.2 \times 10^7}{4 \times 10^3}$ and express the result in standard form.

2. Solution Steps

Problem 4: Simplify $\frac{3 \times 10^2}{5 \times 10^4}$

Step 1: Separate the numerical parts and the powers of

1

0. $\frac{3 \times 10^2}{5 \times 10^4} = \frac{3}{5} \times \frac{10^2}{10^4}$

Step 2: Simplify the numerical part.

$\frac{3}{5} = 0.6$

Step 3: Simplify the powers of 10 using the rule $\frac{a^m}{a^n} = a^{m-n}$.

$\frac{10^2}{10^4} = 10^{2-4} = 10^{-2}$

Step 4: Combine the results.

$0.6 \times 10^{-2}$

Step 5: Express in standard form. Standard form requires the coefficient to be between 1 and

1

0. So, we need to rewrite 0.6 as 6 x 10^{-1}.

$0.6 \times 10^{-2} = (6 \times 10^{-1}) \times 10^{-2} = 6 \times 10^{-1-2} = 6 \times 10^{-3}$

Problem 5: Divide $\frac{1.2 \times 10^7}{4 \times 10^3}$

Step 1: Separate the numerical parts and the powers of

1

0. $\frac{1.2 \times 10^7}{4 \times 10^3} = \frac{1.2}{4} \times \frac{10^7}{10^3}$

Step 2: Simplify the numerical part.

$\frac{1.2}{4} = 0.3$

Step 3: Simplify the powers of 10 using the rule $\frac{a^m}{a^n} = a^{m-n}$.

$\frac{10^7}{10^3} = 10^{7-3} = 10^4$

Step 4: Combine the results.

$0.3 \times 10^4$

Step 5: Express in standard form. Standard form requires the coefficient to be between 1 and

1

0. So, we need to rewrite 0.3 as 3 x 10^{-1}.

$0.3 \times 10^4 = (3 \times 10^{-1}) \times 10^4 = 3 \times 10^{-1+4} = 3 \times 10^3$

3. Final Answer

Problem 4: $6 \times 10^{-3}$

Problem 5: $3 \times 10^3$