Calculate (x×4×3)³: Cube of a Three-Term Product

The power of a product rule states $(ab)^n = a^n b^n$. This works because multiplication is repeated addition, so $(x\cdot4\cdot3)^3$ means multiply the entire product by itself 3 times.

Treat them exactly the same! Whether it's a variable like x or a number like 4, each factor gets raised to the power. Variables become $x^3$ and numbers get calculated like $4^3 = 64$.

No! You can cube each factor separately: $(x\cdot4\cdot3)^3 = x^3\cdot4^3\cdot3^3 = x^3\cdot64\cdot27$. This often makes the work easier than cubing $(12x)^3$.

Simple rule: Everything inside the parentheses gets raised to the power! If it's being multiplied inside those parentheses, it must be raised to the 3rd power.

After applying the rule, you get $x^3\cdot4^3\cdot3^3 = x^3\cdot64\cdot27$. You can multiply the numbers: $64 \times 27 = 1728$, giving you $1728x^3$.