Final answer:
The expression 5⁻⁴ can be written without negative exponents as 1/5⁴ or 1/625, by taking the reciprocal of the base and changing the exponent to positive.
Step-by-step explanation:
To write an equivalent expression without negative exponents, we need to move the base with the negative exponent to the denominator. To convert the expression 5⁻⁴ to an equivalent expression without negative exponents, you simply take the reciprocal of the base raised to the positive of the given negative exponent. Since the base in this expression is 5 and the negative exponent is -4, the equivalent expression without negative exponents would be 1/5⁴, or 1/625.