Final answer:
(1)/(5⁷) can be written with a negative exponent as 5-7. This uses the rule that a negative exponent represents the reciprocal of the base with a positive exponent.
Step-by-step explanation:
To write (1)/(5⁷) with a negative exponent, we use the definition of negative exponents, which states that a negative exponent indicates that the base of the exponent is in the denominator instead of the numerator when written with a positive exponent. Therefore, we can express (1)/(5⁷) as 5-7. This is because any number with a negative exponent is the reciprocal of that number with a positive exponent. In other words, x-n = 1/(xn).
Applying this rule to our initial expression, we transform (1)/(5⁷) into 5-7, which indicates division, as we have moved the base with the positive exponent from the denominator to the numerator and changed the exponent to negative.