Why can #cos^4 θ# be written as #(cos^2 θ)^2# ?

Why can the θ have a square after that?

2 Answers
Jun 18, 2018

As proved below.

Explanation:

As per theory of indices,

#a^m * a^n = a^(m+n)#

#(a^m)^n = a^(mn)#

#cos^4 theta = cos^(2 + 2) theta#

#=> cos^2 theta * cos^2 theta = (cos^2 theta)^2#

Jun 19, 2018

#cos^2 theta# is shorthand for #(cos theta)^2# and #cos^4 theta # is shorthand for #(cos theta)^4.# So,

# cos^4 theta = (cos theta)^4 = ( (cos theta)^2) ^2 = (cos^2 theta)^2#