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DofotheroU

Answered question

2021-08-10

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

Answer & Explanation

ensojadasH

Skilled2021-08-11Added 100 answers

I hope my answer below will help you

Vasquez

Expert2021-12-27Added 669 answers

Step 1

Then given expression can be written as:

$\sqrt[3]{8 x^{3} y^{12}} = (8 x^{3} y^{12})^{\frac{1}{3}} (Since \sqrt[n]{a} = a^{\frac{1}{n}})$

$\sqrt[3]{8 x^{3} y^{12}} (8)^{\frac{1}{3}} (x^{3})^{\frac{1}{3}} (y^{12})^{\frac{1}{3}} (S i n c e (a b)^{m} = a^{m} b^{m})$

$\sqrt[3]{8 x^{3} y^{12}} = (2^{3})^{\frac{1}{3}} (x^{3})^{\frac{1}{3}} (y^{12})^{\frac{1}{3}}$

$\sqrt[3]{8 x^{3} y^{12}} = (2^{3 \times \frac{1}{3}}) (x^{3 \times \frac{1}{3}}) (y^{12 \times \frac{1}{3}}) (Since (a^{m})^{n} = a^{m n})$

$\sqrt[3]{8 x^{3} y^{12}} = (2^{1}) (x^{1}) (y^{4})$

$\sqrt[3]{8 x^{3} y^{12}} = 2 x y^{4}$

Therefore, the given radical expression to its rational exponent form is given by $\sqrt[3]{8 x^{3} y^{12}} = (8 x^{3} y^{12})^{\frac{1}{3}}$ and the simplified form is given by $\sqrt[3]{8 x^{3} y^{12}} = 2 x y^{4}$

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