Find $n$

Algebra Level 1

$\huge \sqrt[n^3]{512} = 2$

What is the value of $n$ ?

3^\dfrac{2}{3}

3^\dfrac{1}{9}

2^\dfrac{2}{3}

3^\dfrac{1}{3}

1 solution

Nazmus Sakib
Nov 16, 2017

$\huge\sqrt[n^3]{512} = 2$

$or,\large (512)^{\dfrac{1}{n^3}}=2$

$or,\large (2^9)^{\dfrac{1}{n^3}}=2$

$or,\large n^3=9$

$or,\large n=(9)^{\dfrac{1}{3}}$

$or,\large n=(3^2)^{\dfrac{1}{3}}$

$or,\large n=(3)^{2\times \dfrac{1}{3}}$

$or,\large n=(3)^{\dfrac{2}{3}}$