`sin^2(2x)cos^2(2x)` Use the power reducing formulas to rewrite the expression in terms of the first power of the cosine.

According to the power reducing formulas, you may re-wrute the expression such that:

`sin^2(2x)*cos^2(2x) = (1 - cos2*(2x))/2*(1 + cos2*(2x))/2`

`sin^2(2x)*cos^2(2x) = ((1 - cos 4x)(1 + cos 4x))/4`

`sin^2(2x)*cos^2(2x) = (1 - cos^2 4x)/4`

`sin^2(2x)*cos^2(2x) = (sin^2 4x)/4`

`sin^2(2x)*cos^2(2x) = ((1 - cos2*(4x))/2)/4`

`sin^2(2x)*cos^2(2x) = (1 - cos 8x)/8`

Hence, eusing the power reducing formulas yields `sin^2(2x)*cos^2(2x) = (1 - cos 8x)/8.`