The problem asks us to select the expressions that are equivalent to the expression $4p + 7p$.

1. Problem Description

The problem asks us to select the expressions that are equivalent to the expression $4p + 7p$.

2. Solution Steps

First, simplify the expression $4p + 7p$. We can combine like terms by adding the coefficients of $p$:

$4p + 7p = (4+7)p = 11p$.

Now we need to check which of the given expressions are equivalent to $11p$.

* $p^{11}$: This means $p$ raised to the power of $11$, which is $p \cdot p \cdot ... \cdot p$ (11 times). This is not equal to $11p$.

* $10p + p$: We can combine like terms again. $10p + p = 10p + 1p = (10+1)p = 11p$. This is equivalent to the original expression.

* $12p$: This is simply $12p$, which is not equal to $11p$.

* $p \cdot 11$: This is equal to $11p$, which is equivalent to the original expression.

Therefore, the expressions equivalent to $4p + 7p$ are $10p + p$ and $p \cdot 11$.

3. Final Answer

The expressions equivalent to $4p+7p$ are $10p+p$ and $p \cdot 11$.