The given expression is:

$(5.36 \times 10^{-4})^3 + (3.13 \times 10^{-5}) \times (2.48 \times 10^{-6})$

We need to calculate this expression using a calculator and give the answer in standard form to 3 significant figures.

Step 1: Calculate $(5.36 \times 10^{-4})^3$

$(5.36 \times 10^{-4})^3 = 5.36^3 \times (10^{-4})^3 = 153.94 \times 10^{-12} = 1.5394 \times 10^{-10}$ (rounded to 5 decimal places for intermediate steps)

Step 2: Calculate $(3.13 \times 10^{-5}) \times (2.48 \times 10^{-6})$

$(3.13 \times 10^{-5}) \times (2.48 \times 10^{-6}) = 3.13 \times 2.48 \times 10^{-5 - 6} = 7.7624 \times 10^{-11}$

Step 3: Add the two results

Now, add the two values calculated:

$1.5394 \times 10^{-10} + 7.7624 \times 10^{-11} = (1.5394 + 0.77624) \times 10^{-10} = 2.31564 \times 10^{-10}$

Step 4: Round the result to 3 significant figures

The result to 3 significant figures is:

$2.32 \times 10^{-10}$

Thus, the final answer is $2.32 \times 10^{-10}$.

Would you like further details or explanations on any of the steps?

Here are 5 related questions to deepen your understanding:

1. How do we simplify powers of 10 when multiplying or raising to a power?
2. Why do we use scientific notation in calculations like this?
3. How can we determine the number of significant figures to use in intermediate steps?
4. What is the importance of rounding in significant figure problems?
5. How would the process change if one of the terms was negative?

Tip: When performing operations involving powers of 10, make sure to handle the exponents separately to simplify calculations.