Question

x^-4/5=81 find x?????​

Answer 1

       

$\huge\boxed{\ \ \ \ \ \ \ \ \ \ \huge\boxed{\ \ \ \ \ \ \ \ \ \huge\boxed{\bold{\ x=3^{-5}}\ }\ \ \ \ \ \ \ \ \ }\ \ \ \ \ \ \ \ \ \ }$

$x^{-\frac{4}{5}}=81 \\ \\ x^{-4 \times \frac{1}{5}}=3^4 \\ \\ (x^{-4})^{\frac{1}{5}}=3^4 \\ \\ (\frac{1}{x^4})^{\frac{1}{5}}=3^4 \\ \\ \\ ((\frac{1}{x^4})^{\frac{1}{5}})^5=(3^4)^5 \\ \\ (\frac{1}{x^4})^{\frac{1}{5} \times 5}=3^{4 \times 5} \\ \\ \frac{1}{x^4}=3^{20}$

$x^4=\frac{1}{3^{20}} \\ \\ x^4=3^{-20} \\ \\ (x^4)^{\frac{1}{4}}=(3^{-20})^{\frac{1}{4}} \\ \\ x^{4 \times \frac{1}{4}}=3^{-20 \times \frac{1}{4}} \\ \\ x=3^{-5}$

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