What is the limit as x approaches infinity of (3^{3*x})/(3^x) ?

The limit as x approaches infinity of (3^{3*x})/(3^x) is infinity

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limit as x approaches infinity of (3^{3*x})/(3^x)

x \to \infty lim (\frac{3 ^{3 \cdot x}}{3 ^{x}})

\infty

Solution steps

x \to \infty lim (\frac{3 ^{3 x}}{3 ^{x}})

Simplify

\frac{3 ^{3 x}}{3 ^{x}} : 9^{x}

= x \to \infty lim (9^{x})

Apply the common limit:

x \to \infty lim (a^{x}) = \infty, a > 1

= \infty

What is the limit as x approaches infinity of (3^{3*x})/(3^x) ?
The limit as x approaches infinity of (3^{3*x})/(3^x) is infinity