9514 1404 393
Answer:
a) z = 2
b) z = 7
Explanation:
a) 3^(z +2) = 81 = 3^4
z +2 = 4 . . . . . . . . . . . equating exponents of the same base
z = 2 . . . . . . . . . subtract 2
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b) 2^-z = 128^-1 = (2^7)^-1 = 2^-7
-z = -7 . . . . . . . equating exponents of the same base
z = 7 . . . . . . multiply by -1
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Additional comment
It is helpful to know the small powers of small numbers like 2 and 3. Squares of numbers to 20 and cubes of numbers to 10 can also be useful to remember.