<s>[INST] Exponential function negative: $\left(\frac{81}{4}\right)^{1/4}\left(\frac{1}4\right)^{-3/4}$ This is another example. $\left(\dfrac{81}{4}\right)^{1/4}\left(\dfrac{1}4\right)^{-3/4}$
Multiply on both sides equals  $\dfrac{81^{1/4}}{4^{1/4}}\cdot \dfrac{1^{-3/4}}{4^{-3/4}}$ 
This should be $\dfrac{3}{4^{1/4}}\cdot \dfrac{1^{-3/4}}{4^{-3/4}}$ which I get to -3/$\sqrt 4^{-1/2}$
Is that correct? I should get the answer 6.
 [/INST] An alternative way (bring everything under a single exponent):
$$(\frac{81}{4})^\frac 14 \cdot (\frac{1}{4})^\frac {-3}{4} = (\frac{81}{4})^\frac 14 \cdot [(\frac 14)^{-3}]^{\frac 14} = (\frac{81}{4})^\frac 14 \cdot(4^{3})^{\frac 14}  = (\frac{81}{4}\cdot 64)^{\frac 14} = (81 \cdot 16)^{\frac 14} = 3 \cdot 2 = 6$$
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