Rewrite the expression as (125^(1/3))^2. The cube root of 125 is 5. Raising 5 to the second power gives 5^2 = 25.

This is equivalent to finding the 5th root of 32 and then squaring it. The 5th root of 32 is 2 (2^5 = 32). Squaring 2 gives 2^2 = 4.

Express as (81^(1/4))^3. The 4th root of 81 is 3 (since 3^4 = 81). Next, cube the result: 3^3 = 27.

Rewrite 64^(5/6) as (64^(1/6))^5. The 6th root of 64 is 2 (since 2^6 = 64). Then, raise 2 to the 5th power: 2^5 = 32.

A fractional exponent m/n means the nth root raised to the mth power. So, 8^(2/3) = (8^(1/3))^2. The cube root of 8 is 2, and 2^2 = 4.

An exponent of 1/3 means finding the cube root. The cube root of 27 is the number that multiplied by itself three times equals 27. Since 3 * 3 * 3 = 27, the answer is 3.

An exponent of 1/2 is equivalent to taking the square root. The square root of 16 is 4, since 4 * 4 = 16.

Apply the negative exponent rule to rewrite as 1 / (-2)^3. Cubing -2 yields -8. Therefore, the result is 1 / -8, which is -1/8.

The exponent -1 simply requires taking the reciprocal of the base. The reciprocal of 1/5 is 5/1, which is just 5.

First, convert negative exponents to fractions: 4^-1 = 1/4. The expression becomes 1/4 + 1/4. Adding these fractions gives 2/4, which simplifies to 1/2.