Final answer:
The expression -3z^-5 can be rewritten without a negative exponent as -3/z^5 by using the reciprocal rule for negative exponents.
Step-by-step explanation:
To rewrite the expression without using a negative exponent, we can use the rule that states an expression with a negative exponent is equal to the reciprocal of the expression with the positive exponent. For the expression -3z^-5, it means we'll take the reciprocal of z raised to the 5th power, and multiply it by -3. So, the rewritten expression is -3/z^5.
This simplification is based on understanding that a negative exponent indicates the inverse of the base raised to the absolute value of the exponent. Thus, the value of the expression does not change, but its form becomes clearer and easier to work with in mathematical operations.