To simplify the given expressions, we can identify the properties used:
1. For the expression **y⁴y²**, we use the **Product of Powers Property**, which states that when multiplying two powers with the same base, you add the exponents. Thus, y⁴y² = y^(4+2) = y⁶.
2. For the expression **x⁻⁵**, we simply recognize that this is already simplified. But if we were to express it positively, we might refer to the **Negative Exponent Rule**, which states that x⁻⁵ = 1/(x⁵).
3. For the expression **(x³)⁶**, we use the **Power of a Power Property**, which states that when raising a power to another power, you multiply the exponents. Thus, (x³)⁶ = x^(3*6) = x¹⁸.
4. For the expression **z³ × z⁵**, we use the **Product of Powers Property** again, which states that when multiplying two powers with the same base, you add the exponents. Thus, z³ × z⁵ = z^(3+5) = z⁸.
To summarize:
- y⁴y²: Product of Powers Property
- x⁻⁵: Negative Exponent Rule (not needed for simplification)
- (x³)⁶: Power of a Power Property
- z³ × z⁵: Product of Powers Property