The problem asks to evaluate the expression $(7 \cdot 8)^3$.

1. Problem Description

The problem asks to evaluate the expression $(7 \cdot 8)^3$.

2. Solution Steps

First, we multiply 7 and

8. $7 \cdot 8 = 56$

Then, we raise the result to the power of

3. $56^3 = 56 \cdot 56 \cdot 56$

$56 \cdot 56 = 3136$

$3136 \cdot 56 = 175616$

Alternatively, we can use the power of a product rule: $(ab)^n = a^n b^n$. Therefore

$(7 \cdot 8)^3 = 7^3 \cdot 8^3 = 343 \cdot 512 = 175616$.

$7^3 = 7 \cdot 7 \cdot 7 = 49 \cdot 7 = 343$

$8^3 = 8 \cdot 8 \cdot 8 = 64 \cdot 8 = 512$

$343 \cdot 512 = 175616$

3. Final Answer

175616