Questions: Simplify: q^4 h^-4 h^4 q^-1 Write your answer with only positive exponents.

Solution Steps

First, combine the terms with the same base. For the base $q$, we have $q^{4}$ and $q^{-1}$. For the base $h$, we have $h^{-4}$ and $h^{4}$.

$$q^{4} h^{-4} h^{4} q^{-1} = q^{4} q^{-1} h^{-4} h^{4}$$

Use the laws of exponents to simplify the expression. Specifically, $a^{m} \cdot a^{n} = a^{m+n}$.

$$q^{4} q^{-1} = q^{4 + (-1)} = q^{3}$$ $$h^{-4} h^{4} = h^{-4 + 4} = h^{0}$$

Any non-zero number raised to the power of 0 is 1. Therefore:

$$h^{0} = 1$$

Now, combine the simplified terms:

$$q^{3} \cdot 1 = q^{3}$$

Final Answer