To convert the given radical expression 4947 to its rational exponent form and then simplify.

Step 1 The given expression can be written as: 4947=7247 4947=(72)147 (Since an=a1n) 4947=(72×14)7 4947(712)7 4947=77 Apply exponent rule; rule a×a=a 4947=7 Therefore, the given radical expression to its rational exponent form is given by 4947=7247 and the simplified form is given by 4947=7

Answered: "To convert the given radical expression 4947 to..."

Lewis Harvey

Answered question

2021-08-10

To convert the given radical expression $\sqrt[4]{49} \sqrt{7}$ to its rational exponent form and then simplify.

Answer & Explanation

cyhuddwyr9

Skilled2021-08-11Added 90 answers

Convertation:

Vasquez

Expert2021-12-28Added 669 answers

Step 1

The given expression can be written as:

$\sqrt[4]{49} \sqrt{7} = \sqrt[4]{7^{2}} \sqrt{7}$

$\sqrt[4]{49} \sqrt{7} = (7^{2})^{\frac{1}{4}} \sqrt{7} (Since \sqrt[n]{a} = a^{\frac{1}{n}})$

$\sqrt[4]{49} \sqrt{7} = (7^{2 \times \frac{1}{4}}) \sqrt{7}$

$\sqrt[4]{49} \sqrt{7} (7^{\frac{1}{2}}) \sqrt{7}$

$\sqrt[4]{49} \sqrt{7} = \sqrt{7} \sqrt{7}$

Apply exponent rule; rule $\sqrt{a} \times \sqrt{a} = a$

$\sqrt[4]{49} \sqrt{7} = 7$

Therefore, the given radical expression to its rational exponent form is given by $\sqrt[4]{49} \sqrt{7} = \sqrt[4]{7^{2}} \sqrt{7}$ and the simplified form is given by $\sqrt[4]{49} \sqrt{7} = 7$

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