Question

(x^2+78x)^1/5=3
Help?

Answer 1

`\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \qquad \sqrt[{ m}]{a^( n)}\implies a^{\frac{{ n}}{{ m}}}\\\\ -----------------------------\\\\ (x^2+78x)^{(1)/(5)}=3\implies \sqrt[5]{(x^2+78x)}=3 \\\\\\ \textit{now, let's raise both sides by 5} \\\\\\\ [\sqrt[5]{(x^2+78x)}]^5=3^5\implies x^2+78x=243\implies x^2+78x-243=0 \\\\\\ \begin{array}{lcclll} x^2&+78x&-243=0\\ &\uparrow &\uparrow \\ &81-3&81\cdot -3 \end{array}\implies (x+81)(x-3)=0`

surely, you'd know what "x" is from there