https://file.aiquickdraw.com/mathbot/file/1726107491382izugotlu.jpg

I see that you have uploaded an image containing several mathematical expressions, mostly involving numbers in scientific notation. Let's go through each of them step by step to solve.

Here are the expressions from the image:

1. **x.** \((2.5 \times 10^3) \times (1.0 \times 10^2)\)

2. **a.** \((4.53 \times 10^3) + (2.2 \times 10^6)\)

3. **b.** \((2.130 \times 10^3) - (6.6 \times 10^2)\)

4. **c.** \((3.5 \times 10^2) \times (6.45 \times 10^{10})\)

5. **d.** \((3.95 \times 10^2) / (1.5 \times 10^6)\)

6. **e.** \((2.5 \times 10^9) / (6.45 \times 10^4)\)

Now, I will solve each one:

### 1. x. \((2.5 \times 10^3) \times (1.0 \times 10^2)\)
\[
= (2.5 \times 1.0) \times (10^3 \times 10^2) = 2.5 \times 10^{3+2} = 2.5 \times 10^5
\]

### 2. a. \((4.53 \times 10^3) + (2.2 \times 10^6)\)
Since the powers of 10 are different, we first rewrite both terms with the same exponent:
\[
4.53 \times 10^3 = 0.00453 \times 10^6
\]
Now, adding them:
\[
0.00453 \times 10^6 + 2.2 \times 10^6 = (0.00453 + 2.2) \times 10^6 = 2.20453 \times 10^6
\]

### 3. b. \((2.130 \times 10^3) - (6.6 \times 10^2)\)
First, convert both terms to have the same exponent:
\[
6.6 \times 10^2 = 0.66 \times 10^3
\]
Now, subtract:
\[
(2.130 - 0.66) \times 10^3 = 1.47 \times 10^3
\]

### 4. c. \((3.5 \times 10^2) \times (6.45 \times 10^{10})\)
\[
= (3.5 \times 6.45) \times (10^2 \times 10^{10}) = 22.575 \times 10^{12} = 2.2575 \times 10^{13}
\]

### 5. d. \((3.95 \times 10^2) / (1.5 \times 10^6)\)
\[
= \frac{3.95}{1.5} \times 10^{2-6} = 2.6333 \times 10^{-4}
\]

### 6. e. \((2.5 \times 10^9) / (6.45 \times 10^4)\)
\[
= \frac{2.5}{6.45} \times 10^{9-4} = 0.3876 \times 10^5 = 3.876 \times 10^4
\]

These are the simplified solutions. Let me know if you'd like more details or have any specific questions!

### Related Questions:

1. How do you multiply and divide numbers in scientific notation?
2. What is the rule for adding or subtracting numbers with different exponents in scientific notation?
3. How do you convert large numbers into scientific notation?
4. What is the difference between significant figures and decimal precision?
5. How do you handle negative exponents in scientific notation?

### Tip:
When adding or subtracting in scientific notation, always adjust the exponents so that both numbers have the same power of 10 before performing the operation.

Solve the following expressions involving numbers in scientific notation: (2.5 x 10^3) x (1.0 x 10^2), (4.53 x 10^3) + (2.2 x 10^6), (2.130 x 10^3) - (6.6 x 10^2), (3.5 x 10^2) x (6.45 x 10^10), (3.95 x 10^2) / (1.5 x 10^6), (2.5 x 10^9) / (6.45 x 10^4).

This page provides step-by-step solutions to common problems in scientific notation, including multiplication, addition, subtraction, and division of numbers with exponents. Learn how to simplify these expressions following the rules of exponents. Suitable for students in Grades 9-12.

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