Questions: Simplify the expression. Write the result using positive exponents only. Assume that all bases are not equal to 0. p^2 * p / p^-4

Solution Steps

The expression in the numerator is \( p^{2} \cdot p \). Using the rule \( p^{a} \cdot p^{b} = p^{a+b} \), we combine the exponents: \[ p^{2} \cdot p = p^{2+1} = p^{3}. \]

Now, the expression becomes: \[ \frac{p^{3}}{p^{-4}}. \]

Using the rule \( \frac{p^{a}}{p^{b}} = p^{a-b} \), we subtract the exponents: \[ \frac{p^{3}}{p^{-4}} = p^{3 - (-4)} = p^{3 + 4} = p^{7}. \]

Final Answer