Answer:
16[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the rule of exponents/ radicals
[tex]a^{\frac{m}{n} }[/tex] = [tex]\sqrt[n]{a^{m} }[/tex] , then
[tex]n^{\frac{2}{3} }[/tex] = [tex]\sqrt[3]{n^2}[/tex] , then
[tex]\sqrt[3]{n^2}[/tex] = 8 ( cube both sides )
n² = 8³ ( take the square root of both sides )
n = [tex]\sqrt{8^3}[/tex]
= [tex]\sqrt{512}[/tex]
= [tex]\sqrt{256(2)}[/tex]
= [tex]\sqrt{256}[/tex] × [tex]\sqrt{2}[/tex]
= 16[tex]\sqrt{2}[/tex]
