\( \begin{array}{lll}\text { 3) } p^{-17} \cdot p & \text { 4) }\left(y^{5}\right)^{7}=y & \text { 5) } \frac{m}{m^{16}}=m^{64}\end{array} \)

Let's take a closer look at each of these expressions and solve them step by step. For the first expression, \( p^{-17} \cdot p \), we can simplify this using the laws of exponents. Remember that \( p \) can be written as \( p^1 \). Therefore, when we multiply, we add the exponents: \[ p^{-17} \cdot p^1 = p^{-17 + 1} = p^{-16}. \] Now, moving on to the second expression \( \left(y^{5}\right)^{7} \). According to the power of a power rule, you multiply the exponents: \[ \left(y^5\right)^7 = y^{5 \cdot 7} = y^{35}. \] Finally, let’s analyze the third expression \( \frac{m}{m^{16}} \). When you divide indices with the same base, you subtract the exponent in the denominator from the exponent in the numerator: \[ \frac{m}{m^{16}} = m^{1 - 16} = m^{-15}. \] If we set this equal to \( m^{64} \), we find \( m^{-15} = m^{64} \). This means we need to have a common exponent; so we can set the bases equal to each other, resulting in the equation: \[ -15 = 64, \] which is impossible. Thus, we have a conflict since there are no values of \( m \) (other than potentially involving complex or undefined numbers) for which this holds true. In summary, we have: 1. \( p^{-16} \) 2. \( y^{35} \) 3. The equation \( m^{-15} = m^{64} \) does not hold true in real numbers.