Simplify the Expression: 5^y × 3^y Using Exponent Properties

To solve this problem, we'll simplify the expression by applying the properties of exponents:

• Step 1: Recognize that both bases, $5$ and $3$, have the same exponent $y$.
• Step 2: Apply the power of a product rule in reverse: for terms $a^y \times b^y$, this simplifies to $(a \times b)^y$.
• Step 3: Replace $a$ with $5$ and $b$ with $3$ to get $(5 \times 3)^y$.

Let's work through the solution with these steps:

Given the expression $5^y \times 3^y$, both terms share the same exponent $y$. Therefore, we can combine them by multiplying the bases and keeping the common exponent:

This simplification follows directly from the rule of exponents, which states $a^n \times b^n = (a \times b)^n$ when $n$ is the same for both terms.

Therefore, the simplified expression is $\left(5 \times 3\right)^y$.