Calculate (4×10×7)^9: Solving a Compound Expression with Exponents

To solve this problem, we'll follow these steps:

• Step 1: Apply the power of a product rule to the given expression.
• Step 2: Evaluate each choice to see if it matches the original expression.

Let's work through the problem:
Step 1: Start with the expression $(4 \times 10 \times 7)^9$. According to the power of a product rule, we can express this as $4^9 \times 10^9 \times 7^9$.

Step 2: Evaluate each answer choice:

• Choice 1: $(40 \times 7)^9$ -> Simplifies to $40^9 \times 7^9$, does not match directly since $10^9$ is missing.
• Choice 2: $(4 \times 70)^9$ -> Simplifies to $4^9 \times 70^9$, does not match directly since $7^9$ is extra.
• Choice 3: a + b are correct -> Considering the intent behind a and b, mixes the choices recognised as potentially correct via simplifications.
• Choice 4: $4 \times 10^9 \times 7^9$ -> is actually incorrect as it has $4$ not raised to the power 9.

Therefore, based on calculation errors observed in each option, the correct conclusion for complex-simplified choices is: a + b (Choice 3) are acknowledged as correct given the correct simplification context.