Calculate the Expression: 5×3⁵×11⁵ Using Powers and Multiplication

To solve the expression $5\times3^5\times11^5$, we can apply the rule of exponents known as the Power of a Product rule. This rule states that for any integers $a$, $b$, and $n$, $(a\times b)^n = a^n \times b^n$.

Step 1: Analyze the expression
The expression we have is $5\times3^5\times11^5$.

Step 2: Apply the Power of a Product rule
Notice that both 3 and 11 are raised to the power of 5. We can use the inverse of the Power of a Product formula to combine these terms:

• $3^5 \times 11^5$ can be written as$(3 \times 11)^5$

Step 3: Rewrite the expression
Therefore, the expression $5\times3^5\times11^5$ becomes $5\times(3\times11)^5$.

By applying the Power of a Product rule, we have determined that the equivalent expression for the given problem is $5\times(3\times11)^5$.