Question

(x2/5)n

For what value of n, written as a decimal, will the expression equal x?

Answer 1

Given:

The expression is:

$\left(x^{\frac{2}{5}\right)^n$

To find:

The decimal value of n so that the value of the given expression is equal to x.

Solution:

We have,

$\left(x^{\frac{2}{5}\right)^n$

This expression is equal to x.

$\left(x^{\frac{2}{5}\right)^n=x$

$x^{\frac{2}{5}n}=x^1$                     $[\because (a^m)^n=a^{mn}]$

On comparing the exponents, we get

$\dfrac{2}{5}n=1$

$2n=5$

$n=\dfrac{5}{2}$

$n=2.5$

Therefore, the required value of n is 2.5.