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