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