Question

Identify the property you would use to simplify each expression. (2 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. y4y2 x−5 (x3)6 z3×z5

Answer 1

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