Let's match each radical expression with its corresponding expression in rational exponent form. We’ll also provide the numerical value for each expression.
1. Radical Expression: [tex]\( 3 \sqrt[4]{50} \)[/tex]
- Rational Exponent Form: [tex]\( 3 \times 50^{1/4} \)[/tex]
- Numerical Value: [tex]\( 7.98 \)[/tex]
2. Radical Expression: [tex]\( 42 \sqrt{2} \)[/tex]
- Rational Exponent Form: [tex]\( 42 \times 2^{1/2} \)[/tex]
- Numerical Value: [tex]\( 59.40 \)[/tex]
3. Radical Expression: [tex]\( 4 \sqrt[3]{7} \)[/tex]
- Rational Exponent Form: [tex]\( 4 \times 7^{1/3} \)[/tex]
- Numerical Value: [tex]\( 7.65 \)[/tex]
4. Radical Expression: [tex]\( 4 \sqrt[5]{3} \)[/tex]
- Rational Exponent Form: [tex]\( 4 \times 3^{1/5} \)[/tex]
- Numerical Value: [tex]\( 4.98 \)[/tex]
5. Radical Expression: [tex]\( 3 \sqrt[5]{4} \)[/tex]
- Rational Exponent Form: [tex]\( 3 \times 4^{1/5} \)[/tex]
- Numerical Value: [tex]\( 3.96 \)[/tex]
6. Radical Expression: [tex]\( 7 \sqrt[4]{38} \)[/tex]
- Rational Exponent Form: [tex]\( 7 \times 38^{1/4} \)[/tex]
- Numerical Value: [tex]\( 17.38 \)[/tex]
Summary:
- [tex]\(3 \sqrt[4]{50} = 3 \times 50^{1/4} = 7.98\)[/tex]
- [tex]\(42 \sqrt{2} = 42 \times 2^{1/2} = 59.40\)[/tex]
- [tex]\(4 \sqrt[3]{7} = 4 \times 7^{1/3} = 7.65\)[/tex]
- [tex]\(4 \sqrt[5]{3} = 4 \times 3^{1/5} = 4.98\)[/tex]
- [tex]\(3 \sqrt[5]{4} = 3 \times 4^{1/5} = 3.96\)[/tex]
- [tex]\(7 \sqrt[4]{38} = 7 \times 38^{1/4} = 17.38\)[/tex]
