Answered

Match each radical expression to the corresponding expression in rational exponent form.

[tex]\[
\begin{array}{|c|c|}
\hline \text{Radical Expression} & \text{Rational Exponent Form} \\
\hline
3 \sqrt[4]{50} & 50^{\frac{1}{4}} \\
\hline
42 \sqrt{2} & 2^{\frac{1}{2}} \\
\hline
4 \sqrt[3]{7} & 7^{\frac{1}{3}} \\
\hline
4 \sqrt[5]{3} & 3^{\frac{1}{5}} \\
\hline
3 \sqrt[5]{4} & 4^{\frac{1}{5}} \\
\hline
7 \sqrt[4]{38} & 38^{\frac{1}{4}} \\
\hline
\end{array}
\][/tex]



Answer :

GinnyAnswer
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]

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