[tex] \sqrt[8]{48^4} [/tex] can be rewritten as [tex] 48^4 [/tex] to the [tex] \frac{1}{8} [/tex] power:
[tex](48^4)^ \frac{1}{8} [/tex]
Now, applying exponent rules (multiply exponent inside parentheses by the one outside parentheses), we get:
[tex](48^ \frac{1}{2}) [/tex]
This is equivalent to [tex] \sqrt{48} [/tex], so now, we just simplify:
[tex] \sqrt{48}= \sqrt{16*3}= \sqrt{16}* \sqrt{3}=4 \sqrt{3}[/tex]
So:
[tex] \sqrt[8]{48^4} =4 \sqrt{3}[/tex]
