![9^{\frac{1}{2} } \cdot 9^{\frac{1}{2} } = \sqrt[x]{81} \\\\\mathrm{Convert\:to\:base\:}9^{\frac{1}{2}}\cdot \:9^{\frac{1}{2}}:\quad 9^{\frac{1}{2}}\cdot \:9^{\frac{1}{2}}=\left(9^{\frac{1}{2}}\cdot \:9^{\frac{1}{2}}\right)^{2\cdot \frac{1}{x}}\\\\9^{\frac{1}{2}}\cdot \:9^{\frac{1}{2}}=\left(9^{\frac{1}{2}}\cdot \:9^{\frac{1}{2}}\right)^{2\cdot \frac{1}{x}}\\\\\mathrm{If\:}a^{f\left(x\right)}=a^{g\left(x\right)}\mathrm{,\:then\:}f\left(x\right)=g(x)\\\\1=2\cdot \frac{1}{x}\\\\Simplify\\](/tpl/images/0785/2986/f070d.png)
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