A group of 300 students were divided into small groups based on their year of birth.
1 answer:
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(9)^4 × (27)^3 × (81)^2 / (3)^24 = 3.
Explanation:
- All the numbers in the numerator i.e. 9, 27, 81 are multiples of 3.
- 9 = 3 × 3 = 3², 27 = 3 × 3 × 3 = 3³, 81 = 3 × 3 × 3 × 3 =
.
= (3^2)^4, 27³ = (3^3)^3, 81^2 = (3^4)^2.
- According to the power rule, (a^x)^y = a^xy.
- So the given numbers can be written as follows
- According to the product rule, (a^x) × (a^y) = a^xy.
- So the numerator can be written as
- So the fraction becomes 3^25 / 3^24 = 3 × 3^24 / 3^24 = 3.