Let's solve this step by step. The given expression is:

(5.36 × 10⁻⁴)³ + (3.13 × 10⁻⁵) × (2.48 × 10⁻⁶)

Step 1: Calculate (5.36 × 10⁻⁴)³

• First, cube 5.36:
  $5.36^3 = 153.509056$
• Then cube 10⁻⁴:
  $(10^{-4})^3 = 10^{-12}$
• Combine:
  $153.509056 \times 10^{-12} = 1.535 \times 10^{-10}$ (rounded to 3 significant figures)

Step 2: Calculate (3.13 × 10⁻⁵) × (2.48 × 10⁻⁶)

• Multiply the numbers 3.13 and 2.48:
  $3.13 \times 2.48 = 7.7624$
• Multiply the powers of 10:
  $10^{-5} \times 10^{-6} = 10^{-11}$
• Combine:
  $7.7624 \times 10^{-11} = 7.76 \times 10^{-11}$ (rounded to 3 significant figures)

Step 3: Add the results

We now add $1.535 \times 10^{-10}$ and $7.76 \times 10^{-11}$:

• Rewrite with the same power of 10 for easier addition:
  $1.535 \times 10^{-10} = 15.35 \times 10^{-11}$
• Add $15.35 \times 10^{-11} + 7.76 \times 10^{-11} = 23.11 \times 10^{-11}$
• Convert back to standard form:
  $23.11 \times 10^{-11} = 2.31 \times 10^{-10}$ (rounded to 3 significant figures)

Final Answer:

$2.31 \times 10^{-10}$

Let me know if you'd like any further clarifications or details! Here are some related questions for practice:

1. What happens if you square instead of cube the first term in this problem?
2. How do you multiply and divide numbers in standard form?
3. What is the importance of expressing results in 3 significant figures?
4. How would the answer differ if $(3.13 \times 10^{-5})$ was replaced with $(4.00 \times 10^{-5})$?
5. How can you check your calculations when using a calculator?

Tip:

When performing operations on powers of 10, always ensure the coefficients (the numbers before $10^x$) are calculated separately before adjusting the powers.