Answer:
The equality is only true for [tex]a = 0\ and\ 1[/tex], not for all values
Step-by-step explanation:
Given
[tex](\sqrt a)^4 = a[/tex]
Required
Determine if it is valid
[tex](\sqrt a)^4 = a[/tex]
Evaluate the exponent
[tex](a^\frac{1}{2})^4 = a[/tex]
[tex]a^\frac{1*4}{2} = a[/tex]
[tex]a^2 = a[/tex]
Rewrite as:
[tex]a^2 - a = 0[/tex]
Factorize
[tex]a(a- 1) = 0[/tex]
[tex]a =0\ or\ a - 1 = 0[/tex]
[tex]a =0\ or\ a = 1[/tex]
The equality is only true for [tex]a = 0\ and\ 1[/tex], not for all values
