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The question asks to find the value of \((7.5 \times 10^4) \times (2.5 \times 10^3)\) and to give the answer in standard form.

### Step 1: Multiply the coefficients
First, multiply the numerical parts (7.5 and 2.5):
\[
7.5 \times 2.5 = 18.75
\]

### Step 2: Multiply the powers of 10
Next, multiply the powers of 10. When multiplying numbers with exponents that have the same base, add the exponents:
\[
10^4 \times 10^3 = 10^{4+3} = 10^7
\]

### Step 3: Combine the results
Now, combine the result from Step 1 and Step 2:
\[
18.75 \times 10^7
\]

### Step 4: Express in standard form
To express this in standard form, the number should be written as \(a \times 10^b\) where \(1 \leq a < 10\). Since 18.75 is greater than 10, we rewrite it as:
\[
18.75 = 1.875 \times 10^1
\]
Thus, the expression becomes:
\[
1.875 \times 10^1 \times 10^7 = 1.875 \times 10^8
\]

### Final Answer:
\[
1.875 \times 10^8
\]

Would you like further details on any step, or do you have any questions?

Here are 5 related questions to expand on this topic:
1. What is standard form, and why is it useful in scientific calculations?
2. How do you divide numbers in scientific notation?
3. Can you explain how to handle negative exponents in multiplication?
4. What happens when you multiply two numbers with different bases in scientific notation?
5. How would the solution change if one of the exponents was negative?

### Tip:
When multiplying numbers in scientific notation, remember to separate the coefficients and powers of 10 to make the calculation simpler.

Work out the value of (7.5 × 10^4) × (2.5 × 10^3). Give your answer in standard form.

Learn how to solve the scientific notation problem (7.5 × 10^4) × (2.5 × 10^3) with a step-by-step guide. This example uses the law of exponents and multiplication of numbers in standard form. Ideal for students in Grades 8-10.

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