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$$(\sqrt[3]{27})^2 =$$
Correct. [[Snippet]] Convert the root to a fractional power (the power is the top of the fraction; the root is the bottom of the fraction): >$$\displaystyle (\sqrt[3]{27})^2 = 27^{\frac{2}{3}}$$. Rewrite 27 as a power of 3: >$$\displaystyle 27^{\frac{2}{3}} = (3^3)^{\frac{2}{3}}$$. Now multiply the exponents and reduce. Remember the rule for a power to an exponent: $$(a^m)^n = a^{mn}$$. >$$\displaystyle (3^3)^{\frac{2}{3}} = 3^{3\times \frac{2}{3}} = 3^2 = 9$$.
$$\sqrt{3}$$
$$3$$
$$9$$
$$\sqrt{27}$$