1. Let's state the problem: We want to understand how to work with expressions where the powers of $x$ are different, for example, one term has $x^3$ (cube) and another has $x^2$ (square). 2. The key formula or rule here is that terms with different powers of $x$ are called unlike terms and cannot be combined by addition or subtraction directly. 3. For example, consider the expression $x^3 + 2x^2$. 4. Since $x^3$ and $x^2$ have different exponents, they are unlike terms and must be left as is when adding or subtracting. 5. However, if you are multiplying or dividing, you can use the laws of exponents: - Multiplying: $x^a \times x^b = x^{a+b}$ - Dividing: $\frac{x^a}{x^b} = x^{a-b}$ 6. For example, $x^3 \times x^2 = x^{3+2} = x^5$. 7. Or $\frac{x^3}{x^2} = x^{3-2} = x^1 = x$. 8. In summary, when powers of $x$ differ: - You cannot add or subtract unlike terms. - You can multiply or divide using exponent rules. This is important to keep expressions simplified correctly.