Question

Given that n^2/3 = 8 and n> 0

Answer 1

Answer:

16$\sqrt{2}$

Step-by-step explanation:

Using the rule of exponents/ radicals

$a^{\frac{m}{n} }$ = $\sqrt[n]{a^{m} }$ , then

$n^{\frac{2}{3} }$ = $\sqrt[3]{n^2}$ , then

$\sqrt[3]{n^2}$ = 8 ( cube both sides )

n² = 8³ ( take the square root of both sides )

n = $\sqrt{8^3}$

   = $\sqrt{512}$

   = $\sqrt{256(2)}$

   = $\sqrt{256}$ × $\sqrt{2}$

   = 16$\sqrt{2}$