Question

Can you explain me one please and solve

Answer 1

`\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \qquad \sqrt[{ m}]{a^( n)}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ (-14)^{(4)/(2)}\implies \sqrt[2]{(-14)^4}\implies √(-14^4) \\\\\\ 8^{(w)/(12)}\implies \sqrt[12]{8^w} \\\\\\ \sqrt[7]{9}\implies \sqrt[7]{9^1}\implies 9^{(1)/(7)} \\\\\\ \sqrt[4]{j^k}\implies j^{(k)/(4)} \\\\\\ \sqrt[12]{(-12)^6}\implies (-12)^{(6)/(12)}\implies (-12)^{(1)/(2)}\\\\ -------------------------------\\\\`


`\bf \sqrt[4]{(-3)^2}\implies (-3)^{(2)/(4)}\implies (-3)^{(1)/(2)}\implies √(-3)\implies √(3\cdot -1) \\\\\\ √(3)\cdot √(-1)\implies i√(3) \\\\\\ -81^{(5)/(4)}\implies -1\cdot 81^{(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`

Answer 2

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.