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

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

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Step 1

Then given expression can be written as:

$$\sqrt[3]{8x^3y^{12}}=(8x^3 y^{12})^{\frac 13} \ \ \ (\text{Since } \sqrt[n]{a}=a^{\frac 1n})$$

$$\sqrt[3]{8x^3y^{12}} (8)^{\frac 13} (x^3)^{\frac 13} (y^{12})^{\frac 13} \ \ \ \ (Since (ab)^m=a^m b^m)$$

$$\sqrt[3]{8x^3 y^{12}}=(2^3)^{\frac 13} (x^3)^{\frac 13} (y^{12})^{\frac 13}$$

$$\sqrt[3]{8x^3y^{12}}=(2^{3 \times \frac 13})(x^{3 \times \frac 13}) (y^{12 \times \frac 13}) \ \ \ (\text{Since } (a^m)^n=a^{mn})$$

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

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

Therefore, the given radical expression to its rational exponent form is given by $$\sqrt[3]{8x^3y^{12}}=(8x^3 y^{12})^{\frac 13}$$ and the simplified form is given by $$\sqrt[3]{8x^3y^{12}}=2xy^4$$