Final answer:
The expression (81^(-1))/4 simplifies to 1/324 by transforming the negative exponent into a positive one through taking the reciprocal of the base and then multiplying by the reciprocal of 4.
Step-by-step explanation:
To simplify the expression using positive exponents, the given expression is (81-1) / 4. An important rule to remember here is that a negative exponent can be turned into a positive one by taking the reciprocal of the base. Therefore, 81-1 can be written as 1/81. Simplifying further:
(81-1) / 4 = (1/81) / 4
To divide by 4, you can multiply by the reciprocal of 4, which is 1/4:
(1/81) * (1/4) = 1 / (81 * 4) = 1 / 324
Therefore, the simplified expression using positive exponents is 1/324.