Simplify the Expression: x⁴·x³/x⁵·x² Using Exponent Rules

Remember that division by the same number equals 1, not 0! When you have $\frac{x^7}{x^7}$, you're dividing identical expressions, which always gives 1 (as long as x ≠ 0).

No! You must follow the order of operations. First use the product rule to simplify the numerator and denominator separately, then apply the quotient rule.

Great question! When x = 0, the original expression becomes $\frac{0}{0}$, which is undefined. The answer x = 1 is only valid when x ≠ 0.

Multiplication = Add exponents ($x^a \cdot x^b = x^{a+b}$)
Division = Subtract exponents ($\frac{x^a}{x^b} = x^{a-b}$)

While $x^0 = 1$ is mathematically correct, the simplified form is just 1. In algebra, we write the simplest form possible, so 1 is preferred over $x^0$.