Evaluate the Expression: (5×3)^6x with Exponential Rules

Insert the corresponding expression:

$\left(5\times3\right)^{6x}=$

To solve this problem, we need to apply the power of a product rule to the given expression, $(5 \times 3)^{6x}$.

According to the exponent rule for the power of a product, when an expression in the form $(a \times b)^n$ is encountered, it can be expanded to $a^n \times b^n$. Here, $a = 5$, $b = 3$, and $n = 6x$.

By applying this rule, we distribute the exponent $6x$ to each of the bases within the parentheses:

• First, apply the exponent to 5, resulting in $5^{6x}$.
• Then, apply the exponent to 3, resulting in $3^{6x}$.

Thus, the expression $(5 \times 3)^{6x}$ simplifies to $5^{6x} \times 3^{6x}$. This shows that the exponent $6x$ is correctly applied to each element within the parentheses.

Therefore, the expression $(5 \times 3)^{6x}$ is equivalent to $5^{6x} \times 3^{6x}$.