№1
а)∛8·27=∛2³·3³=2·3=6
4 4
б) √16·0,0001 = √2^4·(0,1)^4 = 2·0,1=0,2
4 4
в) √625·16 = √5^4·2^4=5·2=10
5 5
г)√0,00032·243 = √(0,2)^5·3^5= 0,2·3=0,6
№2
а)
5 5
√243·1/32=√3^5·1/2^5 = 3·1/2=3/2=1,5
∛24·9=∛2³·3³=2·3=6
4 4 4
√125/0,2 = √ 625 =√ 5^4 =5
∛5^6·2^9 = ∛(5²)³·(2³)³ = 5²·2³=25·8=200
4 4
√ 7^8/3^4= √ (7²)^4 / 3^4 = 7²/3=49/3=16 1/3
б)
∛8/125=∛2³/5³ = 2/5
5 5
√48·162 =√2^5·3^5= 2·3=6
4 4
√16/ 0,0625=√ 2^4/(0,5)^4=2·0,5=1
5 5
√0,2^10·10^10= √(0,2²)^5·(10²)^5 =0,2²·10²=0,04·100=4
∛5^6/3^9= ∛(5²)³/(3³)³=5²·3³=25·27=675
в)
6 6
√64· 1/729=√2^6·1/3^6 = 2·1/3=2/3
∛75·45=∛5³·3³=5·3=15
∛27/0,125=∛3³/0,5³=3/0,5=6
∛0,2³·5^6 =∛0,2³·(5²)³=0,2·5²=5
4 4
√3^12/2^8=√(3³)^4/(2²)^4=3³·2²=108
г)
5 5 5
√ 7 19/32 =√243/32 =√3^·5/2^5 =3/2=1,5
4 4
√54·24 = √ 2^4·3^4=2·3=6
6 6 6
√16/0,25=√ 64 = √ 2^6 = 2
6 6
√36³·2^6 = √ 6^6·2^6=6·2=12
5 5
√5^5/13^10=√5^5/ (13²)^5= 5/13²=5/169