Let's solve the problem from the uploaded image step by step.

We are tasked with evaluating:

$\frac{3.4 \times 10^8 \times 8.2 \times 10^9}{5.7 \times 10^{-3} - 9.6 \times 10^{-4}}$

and presenting the answer in standard form to 2 significant figures.

Step 1: Calculate the numerator

The numerator is:

$3.4 \times 10^8 \times 8.2 \times 10^9$

Multiply the constants $3.4 \times 8.2 = 27.88$. For the powers of 10, add the exponents: $10^8 \times 10^9 = 10^{17}$

So, the numerator becomes: $27.88 \times 10^{17}$

Step 2: Calculate the denominator

The denominator is:

$5.7 \times 10^{-3} - 9.6 \times 10^{-4}$

Convert both terms to the same power of 10. Rewrite $5.7 \times 10^{-3}$ as $57 \times 10^{-4}$. Subtract: $57 \times 10^{-4} - 9.6 \times 10^{-4} = (57 - 9.6) \times 10^{-4} = 47.4 \times 10^{-4}$

Step 3: Combine numerator and denominator

Now divide: $\frac{27.88 \times 10^{17}}{47.4 \times 10^{-4}}$

First, divide the constants: $\frac{27.88}{47.4} \approx 0.588$

For the powers of 10, subtract the exponents: $10^{17} \div 10^{-4} = 10^{21}$

So, the result becomes: $0.588 \times 10^{21}$

Step 4: Convert to standard form

To write this in standard form, shift the decimal point of $0.588$ one place to the right, which increases the power of 10 by 1: $5.88 \times 10^{20}$

Step 5: Round to 2 significant figures

The rounded result is: $5.9 \times 10^{20}$

Final Answer:

$5.9 \times 10^{20}$

Would you like a detailed breakdown of any step?
Here are 5 questions related to this problem for further practice:

1. How do you handle subtraction involving powers of 10?
2. What are the rules for multiplying numbers in scientific notation?
3. How do you simplify expressions like $10^8 \times 10^9$?
4. What is the importance of writing results in standard form?
5. How do you round a number to a specific number of significant figures?

Tip: Always align the exponents before performing addition or subtraction with numbers in scientific notation.