Summative Unit 5: Rational Exponents N.RN.A.2(10PTS) A.REI.A.2(10PTS) F.BF.B.3(25PTS) NAME $$ \qquad $$ BLOCK $$ \qquad $$ A)[N.RN.A.2][4 PTS] DIRECTIONS: Rewrite each expression. If given in radical form, rewrite in exponential form and vice versa. 1) $$ (\sqrt[3]{x})^{2} $$ 2) $$ (2 x)^{\frac{3}{2}} $$ 3) $$ \sqrt[5]{7 x} $$ 4) $$ (2 x)^{\frac{2}{5}} $$

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1) Empezamos con $$ (\sqrt[3]{x})^{2} $$. Recordamos que $$\sqrt[3]{x}=x^{\frac{1}{3}}$$. Entonces:
$$
(\sqrt[3]{x})^{2} = \left(x^{\frac{1}{3}}\right)^{2} = x^{\frac{2}{3}}
$$

2) Tenemos $$ (2x)^{\frac{3}{2}} $$ en forma exponencial. Para expresarlo en forma radical, usamos la propiedad:
$$
(2x)^{\frac{3}{2}} = \sqrt{(2x)^3} = \sqrt{8x^3}
$$

3) La expresión $$ \sqrt[5]{7x} $$ se puede escribir en forma exponencial como:
$$
\sqrt[5]{7x} = (7x)^{\frac{1}{5}}
$$

4) Finalmente, $$ (2x)^{\frac{2}{5}} $$ se puede expresar en forma radical aplicando la propiedad:
$$
(2x)^{\frac{2}{5}} = \sqrt[5]{(2x)^2} = \sqrt[5]{4x^2}
$$
1) $$ (\sqrt[3]{x})^{2} = x^{\frac{2}{3}} $$ 2) $$ (2x)^{\frac{3}{2}} = \sqrt{8x^3} $$ 3) $$ \sqrt[5]{7x} = (7x)^{\frac{1}{5}} $$ 4) $$ (2x)^{\frac{2}{5}} = \sqrt[5]{4x^2} $$

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