Expand (2a)^(y+5): Step-by-Step Expression Expansion

To solve the problem of expanding $(2a)^{y+5}$, we'll use the Power of a Product Rule.

• Step 1: Identify the base and the exponent. Here, the base is $2a$, and the exponent is $y+5$.
• Step 2: Apply the Power of a Product Rule, which states that $(ab)^n = a^n \times b^n$. In this case, apply it to the base $2a$.
• Step 3: Expand the expression: $(2a)^{y+5} = 2^{y+5} \times a^{y+5}$.

By applying the rule, we separate the exponential expression into two parts, one for each component of the base:

$(2a)^{y+5} = 2^{y+5} \times a^{y+5}$

This result shows that both $2$ and $a$ are individually raised to the power of $y+5$. The application of the product rule ensures that each base component is treated equally within the exponentiation.

Therefore, the expanded form of the expression is $2^{y+5} \times a^{y+5}$, which corresponds to answer choice 4.