Respuesta :

Lets start with number 1. (-14)^4/2. so we know from the start that 4/2 is 2. So the answer is (-14)^2. Another way to solve this problem is by converting it to square root form. We see that (-14)^4/2 can be written as the square root of (-14)^4. We know this because the top part of the exponential fraction is the actually exponential value and the denominator is the root. Using either way, we get that the answer is (-14)^2.
[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ (-14)^{\frac{4}{2}}\implies \sqrt[2]{(-14)^4}\implies \sqrt{-14^4} \\\\\\ 8^{\frac{w}{12}}\implies \sqrt[12]{8^w} \\\\\\ \sqrt[7]{9}\implies \sqrt[7]{9^1}\implies 9^{\frac{1}{7}} \\\\\\ \sqrt[4]{j^k}\implies j^{\frac{k}{4}} \\\\\\ \sqrt[12]{(-12)^6}\implies (-12)^{\frac{6}{12}}\implies (-12)^{\frac{1}{2}}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \sqrt[4]{(-3)^2}\implies (-3)^{\frac{2}{4}}\implies (-3)^{\frac{1}{2}}\implies \sqrt{-3}\implies \sqrt{3\cdot -1} \\\\\\ \sqrt{3}\cdot \sqrt{-1}\implies i\sqrt{3} \\\\\\ -81^{\frac{5}{4}}\implies -1\cdot 81^{\frac{5}{4}}\implies -1\cdot \sqrt[4]{81^5}\qquad \boxed{81=3^4}\qquad thus \\\\\\ -1\cdot \sqrt[4]{(3^4)^5}\implies -\sqrt[4]{(3^5)^4}\implies -3^5\implies -243[/tex]

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