Verified answer

a^m * a^n = a^(m + n)

√a = a^1/2  a>0

1/a = a^-1

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11.11

y = 2^x

a. 16 = 2^4   x = 4

b. 8√2 = 2^3 * 2^1/2 = 2^3.5    x = 7/2 = 3.5

c. 1/√2 = 1/2^1/2 = 2^-1/2     x = -1/2 = -0.5

d. 1/(32√2) = 1/(2^5*2^1/2) = 1/2^2.5 = 1^-2.5     x=-5/2 = -2.5

11.12

y = (1/5)^x

a. 1/25 = (1/5)^2     x = 2

b. 1/(25√5) = 1/(5^2*5^1/2) = 1/(5^2.5)    x = 5/2 = 2.5

c. 125 = 5^3 = 1/5^-3   x = -3

d. 625√5 = 5^4*5^1/2 = 5^4.5 = 1/5^-4.5   x = -9/2 = -4.5