16 = 2^(4), so x = 4.

32 = 2^(5), so x = 5.

81 = 3^(4), so x = 4.

a/b = 2^(3)/2^(2) = 2^(3-2) = 2^(1).

a^(b+1) = 3^(2+1) = 3^3 = 27.

a^4 = (3^(1/2))^4 = 3^2 = 9.

b^6 = (2^(1/3))^6 = 2^2 = 4.

x/y = 2^(3)/2^(4) = 2^(3-4) = 2^(-1) = 1/2.

x^4 = (2^(3/4))^4 = 2^3 = 8.

x = √(25) = 5, thus x^2 = 5^2 = 25.

√(2) * √(8) = √(16) = 4, but simplified is 2√(2).

√(a^2) * √(b^2) = ab.

Using the property (a^m)^n = a^(m*n), we have (3^(2))^(3) = 3^(2*3) = 3^(6).

√(2) * √(8) = √(16) = 4.

(√(2) + √(3))^2 = 2 + 3 + 2√(6) = 5 + 2√(6).

(√(3) + √(2))^2 = 3 + 2 + 2√(6) = 5 + 2√(6).

4^(1/2) = 2, thus 2 * 2 = 4.

4^(1/2) = √(4) = 2.

4^(3/2) = (√4)^3 = 2^3 = 8.

Any non-zero number raised to the power of 0 is 1.

9^(1/2) = 3 and 16^(1/2) = 4, so 3 + 4 = 7.

√(16) = 4 and √(9) = 3, so 4 + 3 = 7.

√(25) = 5 and √(16) = 4, so 5 - 4 = 1.

5^(2/3) = (5^(1/3))^2 = 5√(5).

Using the power of a power property, (x^(1/2))^4 = x^(1/2 * 4) = x^(2).

Using the property a^m * a^n = a^(m+n), we have 2^(3+2) = 2^(5).

2^(3/2) = √(2^3) = √8.

27 = 3^(3), so 2x = 3, thus x = 3/2.

16 = 4^(2), thus x = 2.

25 = 5^(2), thus x = 2.