How do you simplify (x^3)^4?

To simplify \((x^3)^4\), you multiply the exponents to get \(x^{12}\).

When simplifying expressions with exponents, one of the key rules to remember is the power of a power rule. This rule states that when you have an exponent raised to another exponent, you multiply the exponents together. In mathematical terms, \((a^m)^n = a^{m \cdot n}\).

In the expression \((x^3)^4\), the base \(x\) is raised to the power of 3, and then this entire term is raised to the power of 4. According to the power of a power rule, you multiply the exponents 3 and 4 together. So, \(3 \times 4 = 12\). Therefore, \((x^3)^4\) simplifies to \(x^{12}\).

This rule is very useful when dealing with more complex algebraic expressions and helps to keep your work neat and manageable. Always remember to multiply the exponents when you see a power raised to another power. This will make your calculations quicker and more accurate.