Solve Exponential Equations

[nycmath]

See attachment.

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[tex]9^{2x} \cdot 27^{x^2} = 3^{-1}[/tex]

[tex]9 = 3^2[/tex], [tex]27 = 3^3[/tex]

[tex]3^{4x} \cdot 3^{3x^2} = 3^{-1}[/tex]

[tex]3^{3x^2 + 4x} = 3^{-1}[/tex]
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[tex]3x^2 + 4x + 1 = 0[/tex]

[tex](3x + 1)(x + 1) = 0[/tex]

[tex]x = -\frac{1}{3} \quad \text{or} \quad x = -1[/tex]

Check [tex]x = -1[/tex]: [tex]9^{-2} \cdot 27 = \frac{27}{81} = \frac{1}{3}[/tex]

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Question A:

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Question B:

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Question C: