How would I simplify the following radical.

$$\large \sqrt[12]{64a^{3}b^{6}}$$

I know that I can do

$$\large 64^{\frac{1}{12}}a^{\frac{3}{12}}b^{\frac{6}{12}}$$

But I am unsure how to simplify it further.

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$$\sqrt[\large 12]{64a^{3}b^{6}}= (64)^{1/12}a^{3/12}b^{6/12} = (2^6)^{1/12}a^{1/4}b^{1/2} = 2^{6/12}a^{1/4}b^{1/2} = 2^{1/2}a^{1/4}b^{1/2} = (2b)^{1/2}a^{1/4}$$
Yes, exactly! $\sqrt{2b}\cdot \sqrt[\large 4]{a}$ which can also be expressed as $\sqrt[\large 4]{4b^2a}$ –  amWhy Jan 17 '13 at 17:27