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Bunuel
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If (243^(9 + 18z))(81^(-18z))(27^15 - 9z) = 1, what is the value of z? 16 Jan 2021, 10:24
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D
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74% (02:26) correct 26% (02:57) wrong based on 101 sessions

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If \((243^{9 + 18z})(81^{-18z})(27^{15 - 9z}) = 1\), what is the value of z?

A) -27
B) -10
C) 0
D) 10
E) 27
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D
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If (243^(9 + 18z))(81^(-18z))(27^15 - 9z) = 1, what is the value of z? 16 May 2021, 02:45
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Bunuel
If \(243^{9 + 18z}*81^{-18z}*27^{15 - 9z} = 1\), what is the value of z?

(A) -27
(B) -10
(C) 0
(D) 10
(E) 27
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\(243^{(9 + 18z)}*81^{(-18z)}*27^{(15 - 9z)} = 1\)

243 = 3^5, 81 = 3^4 and 27 = 3^3, hence \(3^{5(9 + 18z)}*3^{4(-18z)}*3^{3(15 - 9z)} = 1\)

\(3^{5(9 + 18z)+4(-18z)+3(15 - 9z)} = 1\). This implies that the power of 3 must be 0.

Therefore \(5(9 + 18z)+4(-18z)+3(15 - 9z)=0\) --> \(z= 10\).

Answer: D.
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If (243^(9 + 18z))(81^(-18z))(27^15 - 9z) = 1, what is the value of z? 16 Jan 2021, 20:19
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Bunuel
If \((243^{9 + 18z})(81^{-18z})(27^{15 - 9z}) = 1\), what is the value of z?

A) -27
B) -10
C) 0
D) 10
E) 27
Show more


The powers of 3 : \(3^1=3 \ \ 3^2=9 \ \ 3^3=27 \ \ 3^2=81 \ \ 3^5=243\)

\((243^{9 + 18z})(81^{-18z})(27^{15 - 9z}) = 1\)
\(((3^5)^{9 + 18z})((3^4)^{-18z})((3^3)^{15 - 9z}) = 1\)
\((3^{45 + 90z})(3^{-72z})(3^{45 - 27z}) = 1\)
\((3^{45 + 90z-72z+45 - 27z}) = 3^0\)
Equating the powers
\(45 + 90z-72z+45 - 27z=0\)
\(90-9z=0....z=10\)

D

You could also do by substitution from options
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If (243^(9 + 18z))(81^(-18z))(27^15 - 9z) = 1, what is the value of z? 10 May 2021, 19:12
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Bunuel
If \(243^{9 + 18z}*81^{-18z}*27^{15 - 9z} = 1\), what is the value of z?

(A) -27
(B) -10
(C) 0
(D) 10
(E) 27
Show more

Given: \(243^{9 + 18z}*81^{-18z}*27^{15 - 9z} = 1\).
z =?

\(243 = 3^5, 81 = 3^4\) and \(27 = 3^3\)

=> \(243^{9 + 18z}*81^{-18z}*27^{15 - 9z} = 3^{5 * (9 + 18z)}*3^{4*(-18z)}*3^{3*(15 - 9z)} = 3^0 \)
=> 45 + 90z - 72z + 45 - 27z = 0
=> 9z = 90
=> z = 10

So, correct answer is option D.
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If (243^(9 + 18z))(81^(-18z))(27^15 - 9z) = 1, what is the value of z? 10 May 2021, 21:07
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If \(243^{9 + 18z}*81^{-18z}*27^{15 - 9z} = 1\), what is the value of z?

(A) -27
(B) -10
(C) 0
(D) 10
(E) 27
Show more
\(243^{9 + 18z}*81^{-18z}*27^{15 - 9z} = 1\)
\(3^{5*(9 + 18z)}*3^{4*(-18z)}*3^{3*(15 - 9z)} = 1\)
\(3^{45}*3^{90z}*3^{-72z}*3^{45}*3^{- 27z} = 1\)
\(\frac{3^{90+90z}}{3^{99z}} = 1\)
\(\implies\) 90+90z = 99z
z = 10

Answer D.
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If (243^(9 + 18z))(81^(-18z))(27^15 - 9z) = 1, what is the value of z? 11 May 2021, 06:56
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Convert all in the powers of 3 and apply exponents logic:

I. \(x^a * x^b = x ^{a + b}\)

II. \((x^a)^b = x^{ab}\)

III. \(x^0 = 1\)

IV. When bases are the same, powers are equal.


=> \(243 = 3^5: 243^{9 + 18z} = (3^5)^{9 + 18z} =(3)^{45 + 90z}\)

=> \(81 = 3^4: 81^{-18z} = (3^4)^{-18z} =(3)^{- 72z}\)

=> \(27 = 3^3: 27^{15 - 9z} = (3^3)^{15 - 9z} =(3)^{45 - 27z}\)

=> \(243^{9 + 18z} * 81^{-18z} * 27^{15 - 9z} = 1\)

=> \((3)^{45 + 90z} * (3)^{- 72z} * (3)^{45 - 27z} = 1\)

=> \((3)^{45 + 90z -72z + 45 - 27z} = 1\)

=> \((3)^{90-9z} = 3^0\)

=> \(90 - 9z = 0\)

=> \(z = 10\)

Answer D
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If (243^(9 + 18z))(81^(-18z))(27^15 - 9z) = 1, what is the value of z? 21 Jan 2026, 10:07
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