To convert the given radical expression 943 to its rational exponent form and then simplify

Step 1 The given expression can be written as: 943=3243 943=(32)143 (Since an=a1n) 943=(32×14)3 943=(312)3 943=33 Apply exponent rule; rule a×a=a 943=3 Therefore, the given radical expression to its rational exponent form is given by 943=(32)143 and the simplified form is given by 943=3

Expert answers to "To convert the given radical expression 943 to..."

ediculeN

Answered question

2021-08-06

To convert the given radical expression $\sqrt[4]{9} \sqrt{3}$ to its rational exponent form and then simplify

Answer & Explanation

gotovub

Skilled2021-08-07Added 98 answers

Given that:

Vasquez

Expert2021-12-28Added 669 answers

Step 1

The given expression can be written as:

$\sqrt[4]{9} \sqrt{3} = \sqrt[4]{3^{2}} \sqrt{3}$

$\sqrt[4]{9} \sqrt{3} = (3^{2})^{\frac{1}{4}} \sqrt{3} (Since \sqrt[n]{a} = a^{\frac{1}{n}})$

$\sqrt[4]{9} \sqrt{3} = (3^{2 \times \frac{1}{4}}) \sqrt{3}$

$\sqrt[4]{9} \sqrt{3} = (3^{\frac{1}{2}}) \sqrt{3}$

$\sqrt[4]{9} \sqrt{3} = \sqrt{3} \sqrt{3}$

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

$\sqrt[4]{9} \sqrt{3} = 3$

Therefore, the given radical expression to its rational exponent form is given by $\sqrt[4]{9} \sqrt{3} = (3^{2})^{\frac{1}{4}} \sqrt{3}$ and the simplified form is given by $\sqrt[4]{9} \sqrt{3} = 3$

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