ensojadasH

Answered 2021-08-11
Author has **16275** answers

Vasquez

Answered 2021-12-27
Author has **10020** answers

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

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To determine: The radical form of \(\displaystyle{x}^{{2}}\sqrt{{{x}}}\) in the rational exponent form.