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If (2439 + 18z)(81-18z)(2715 - 9z) = 1, what is the value of z?
Correct Answer: D
How can the number 1 be written to have a base of 3 and an exponent?
  1. Rewrite the terms on the left-side with common prime bases.
    (2439 + 18z)(81-18z)(2715 – 9z)
    = (35(9 + 18z))(34(-18z))(33(15 – 9z))
    = (345 + 90z)(3-72z)(3(45 – 27z))
  2. Simplify by combining terms with like bases.
    (345 + 90z)(3-72z)(3(45 – 27z))
    = 345 + 45 + 90z – 72z – 27z
    = 390 -9z
  3. As a result of this simplification, the equation is much easier to deal with.
    390 -9z = 1
  4. At this point, the problem may appear unsolvable as different bases and exponents exist. However, remember that any number raised to the 0th power is 1. Consequently, 1 can be rewritten as 30. The equation now reads:
    390 -9z = 1
    390 -9z = 1 = 30
  5. Since the bases are the same, you can set the exponents equal to each other. The equation becomes:
    90 – 9z = 0
    90 = 9z
    z = 10

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