the number of prime factors in expression 6^4×8^6
Answers
Answer:
Step-by-step explanation:
(6)4×(8)6×(10)8×(12)10=(2×3)4×(23)6×(2×5)8×(22×3)10=24×34×218×28×58×220×310=24+18+8+20×34+10×58 (Since am×an=am+n)=250×314×58Here prime factors are 2 , 3 and 5 .Number of prime factors=50+14+8=72 ANS...
Answer:
72.
Step-by-step explanation:
We solve the given expression as follows:
(6)
4
×(8)
6
×(10)
8
×(12)
10
=(2×3)
4
×(2
3
)
6
×(2×5)
8
×(2
2
×3)
10
=(2
4
×3
4
)
4
×(2
18
)
6
×(2
8
×5
8
)
8
×(2
20
×3
10
)
10
=2
4
×3
4
×2
18
×2
8
×5
8
×2
20
×3
10
=2
4+18+8+20
×3
4+10
×5
8
{∵a
m
×a
n
=a
m+n
}
=2
50
×3
14
×5
8
Here, the prime factors are 2,3 and 5, therefore, the number of prime factors are:
50+14+8=72
Hence, the number of prime factors is 72.