Pronunciation: [stɹˈɛnjuːəsliz] (IPA)
Correct spelling for the English word "strenuouslies" is [stɹˈɛnjuːəsliz], [stɹˈɛnjuːəsliz], [s_t_ɹ_ˈɛ_n_j_uː_ə_s_l_i_z] (IPA phonetic alphabet).
Correct spelling for strenuouslies