A. Express the following in radical form. B. Express the following with rational exponent. 1. \( 5^{\frac{3}{4}} \) 2. \( (3 x y)^{\frac{2}{3}} \) _ 3. \( 6 a^{\frac{3}{5}} \)

Certainly! Let's address each part of the problem step by step. --- ### **1. \( 5^{\frac{3}{4}} \)** #### **A. Expressed in Radical Form:** \[ 5^{\frac{3}{4}} = \sqrt[4]{5^3} = \sqrt[4]{125} \] #### **B. Expressed with Rational Exponent:** \[ 5^{\frac{3}{4}} \] *(Already given in rational exponent form.)* --- ### **2. \( (3xy)^{\frac{2}{3}} \)** #### **A. Expressed in Radical Form:** \[ (3xy)^{\frac{2}{3}} = \sqrt[3]{(3xy)^2} = \sqrt[3]{9x^2y^2} \] #### **B. Expressed with Rational Exponent:** \[ (3xy)^{\frac{2}{3}} \] *(Already given in rational exponent form.)* --- ### **3. \( 6a^{\frac{3}{5}} \)** #### **A. Expressed in Radical Form:** \[ 6a^{\frac{3}{5}} = 6 \cdot \sqrt[5]{a^3} \] #### **B. Expressed with Rational Exponent:** \[ 6a^{\frac{3}{5}} \] *(Already given in rational exponent form.)* --- ### **Summary:** | **Expression** | **A. Radical Form** | **B. Rational Exponent** | |-------------------------|------------------------------|------------------------------| | \( 5^{\frac{3}{4}} \) | \( \sqrt[4]{125} \) | \( 5^{\frac{3}{4}} \) | | \( (3xy)^{\frac{2}{3}} \)| \( \sqrt[3]{9x^2y^2} \) | \( (3xy)^{\frac{2}{3}} \) | | \( 6a^{\frac{3}{5}} \) | \( 6\sqrt[5]{a^3} \) | \( 6a^{\frac{3}{5}} \) | --- Feel free to reach out if you have any further questions or need additional clarifications!