# To convert the given radical expression \sqrt[3]{x^{12}} to its rational exponent form and then simplify

Jason Farmer 2021-08-08 Answered

To convert the given radical expression $$\sqrt[3]{x^{12}}$$ to its rational exponent form and then simplify

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## Expert Answer

rogreenhoxa8
Answered 2021-08-09 Author has 26324 answers
Now we have
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Vasquez
Answered 2021-12-28 Author has 10750 answers

Step 1

The given expression can be written as:

$$\sqrt[3]{x^{12}}=(x^{12})^{\frac 13} \ \ \ \ (\text{ Since } \sqrt[n]{a}=a^{\frac 1n})$$

$$\sqrt[3]{x^{12}}=(x^{12 \times \frac 13}) \ \ \ (\text{ Since } (a^m)^n=a^{mn})$$

$$\sqrt[3]{x^{12}}=(x^{\frac{12}{3}})$$

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

Therefore, the given radical expression to its rational exponent form is given by $$\sqrt[3]{x^{12}}=(x^{12})^{\frac 13}$$ and the simplifiend form is given by $$\sqrt[3]{x^{12}}=x^4$$

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