1)
81=3 la puterea 4
81=9²
2)
[(2³·Ala puterea(-2)·B la puterea (-1))/24A·Bla puterea (-2)]la puterea(-1)=
=[2³·Ala puterea(-2)·B la puterea(-1):2³·3·A·B la puterea(-2)]la puterea(-1)=
=[2la puterea (3-3)·3·A la puterea (-2-1)·B la puterea (-1+2)]la puterea -1=
=[2la puterea 0·3·A la puterea -3·B]laputerea (-1)=
=3la puterea (-1)·Ala puterea (-3)·(-1)·Bla puterea (-1)=
=A³/3B
3)√(-2x+3)
-2x+3≥0
-2x≥-3 (-1)
x≤3/2
x∈(-α,3/2]
4)
√(52²-48²)=√(2²·13-2 l puterea 4·3)=√2²(13-2²·3)=√2²(13-12)=√2²=2
5)
√48=√(2la puterea 4·3)=4√3
13√(12/25)=13√(2²·3)/5²=13·2√3/5=26√3/5
√4intreg 8/25=√108/25=√(2²·3)/√5²=6√3/5
=4√3-26√3/5+6√3/5=4√3-20√3/5=4√3-4√3=0
b)
=(11la puterea 1/2+6la puterea 1/2·2la puterea 1/4-11 la puterea 1/2+6 la puterea 1/2·2la puterea 1/4]²=
=[6la puterea1/2·2la puterea 1/4(1+1)]²=
=6 la puterea 2/2·2 la puterea 2/4·2²=
=6·2la puterea (2/4+2)=
=6·2 la puterea 5/2=12√2
