How can I simplify #((f^-16)/(256g^4h^-4))^(-1/4)#?
2 Answers
Very slightly different approach.
Explanation:
Given:
The trick is to remember that anything raised to a negative power is inverted
Rewrite as:
Rewrite as:
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
For method think of:
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Giving:
Explanation:
If
Also
Hence we find:
#((f^(-16))/(256g^4h^(-4)))^(-1/4)=((256g^4h^(-4))/(f^-16))^(1/4)=((4^4f^16g^4)/(h^4))^(1/4)#
#=((4^4(f^4)^4g^4)/(h^4))^(1/4)=(((4f^4g)/h)^4)^(1/4)=abs((4f^4g)/h)#
If
Hence for any