Answered

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(x2/5)n

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

Sagot :

Given:

The expression is:

[tex]\left(x^{\frac{2}{5}\right)^n[/tex]

To find:

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

Solution:

We have,

[tex]\left(x^{\frac{2}{5}\right)^n[/tex]

This expression is equal to x.

[tex]\left(x^{\frac{2}{5}\right)^n=x[/tex]

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

On comparing the exponents, we get

[tex]\dfrac{2}{5}n=1[/tex]

[tex]2n=5[/tex]

[tex]n=\dfrac{5}{2}[/tex]

[tex]n=2.5[/tex]

Therefore, the required value of n is 2.5.

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