Final answer:
1/81 and 1/63 can be written as powers of their prime factors with negative exponents: 1/81 is 3^-4, and 1/63 is 3^-2 * 7^-1.
Step-by-step explanation:
To express 1/81 and 1/63 without using a fraction bar and using exponents, we can rewrite them as powers of their prime factors. The number 81 can be expressed as 3^4 (since 3 * 3 * 3 * 3 = 81), and similarly, 63 can be written as 3^2 * 7 (because 3 * 3 * 7 = 63). Hence, 1/81 can be written as 3^-4 and 1/63 can be written as 3^-2 * 7^-1. The negative exponent indicates that the number is on the bottom of a fraction, and when written without a fraction bar, that number is 'raised to the power of the negative of that exponent'.