To express the given number in index form, we have to decompose the number as prime factors.
If we have repeated values, using exponents we can write down it.
For example,
5 x 5 x 5 = 5^{3}
Express the following as the product of prime factors in index form:
Problem 1 :
56
Solution :
56 = 8 × 7
= 2 × 2 × 2 × 7
= 2^{3} × 7
Problem 2 :
240
Solution :
240 = 16 × 15
= 4 × 4 × 3 × 5
= 2^{ }× 2 × 2 × 2 × 3 × 5
= 2^{4} × 3 × 5
Problem 3 :
504
Solution :
504 = 72 × 7
= 8 × 9 × 7
= 2 × 2 × 2 × 3 × 3 × 7
= 2^{3} × 3² × 7
Problem 4 :
735
Solution :
735 = 15 × 49
= 3 × 5 × 7 × 7
= 3 × 5 × 7²
Problem 5 :
297
Solution :
297 = 27 × 11
= 9 × 3 × 11
= 3 × 3 × 3 × 11
= 3^{3} × 11
Problem 6 :
221
Solution :
221 = 13 × 17
Problem 7 :
360
Solution :
360 = 72 × 5
= 8 × 9 × 5
= 2 × 2 × 2 × 3 × 3 × 5
= 2^{3} × 3² × 5
Problem 8 :
952
Solution :
952 = 56 × 17
= 8 × 7 × 17
= 2 × 2 × 2 × 7 × 17
= 2^{3} × 7 × 17
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM