Simplify the Expression: 5^(y+1) × 3^(y+1) Product Rule Challenge

To solve this problem, we'll use the "Power of a Product" rule.

We begin with the expression $5^{y+1} \times 3^{y+1}$.

Notice that both terms share the same exponent, $y+1$.

According to the Power of a Product rule, $a^m \times b^m = (a \times b)^m$. This means we can combine $5^{y+1} \times 3^{y+1}$ into a single expression.

Let's apply the formula:

• Identify each base: $a = 5$ and $b = 3$.

• The shared exponent is $m = y+1$.

• Substitute into the formula: $(5 \times 3)^{y+1}$.

Therefore, the corresponding expression is $\left(5 \times 3\right)^{y+1}$.