Question

simplify the following expression.

\\ (\sqrt9{27})^3 \\

\\ (\sqrt9{27})^3 = \square \\ (type an exact answer, using radicals

Explanation:

⚡ Using what you learned: Integer and Rational Exponents

Step 1: Convert to rational exponents

$$ (\sqrt[9]{27})^3 = (27^{\frac{1}{9}})^3 = 27^{\frac{3}{9}} = 27^{\frac{1}{3}} $$

Step 2: Simplify the base

$$ 27 = 3^3 $$

$$ (3^3)^{\frac{1}{3}} = 3^{3 \cdot \frac{1}{3}} = 3^1 = 3 $$

Answer:

3