Final answer:
To simplify (6/t^{-4}), recognize t^{-4} as 1/t^4 and multiply 6 by t^4, resulting in the simplified expression 6t^4.
Step-by-step explanation:
To use the quotient rule to simplify the expression (6/t^{-4}), where t ≠ 0, we first recognize that a negative exponent indicates the reciprocal of the base raised to the positive exponent. Therefore, t^{-4} is the same as 1/t^4. When we divide 6 by 1/t^4, it is equivalent to multiplying 6 by t^4.
The simplified expression is:
6 × t^4 or 6t^4.
Remember that when dividing by a term with a negative exponent, you can move the term to the numerator and change the sign of the exponent, then multiply as usual.