Question

How is the equation on the top equivalent to 3. Show 5 steps on how you did it.

Answer 1

(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 = $3^{4}$.
• $9^{4}$ = (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                                                         $9^{4}$ = 3^8, 27³ = 3^9 and 81² = 3^8.
• According to the product rule, (a^x) × (a^y) = a^xy.
• So the numerator can be written as                                                                             $9^{4}$ × 27³ × 81² = (3^8) × (3^9) × (3^8) = 3^(8+9+8) = 3^25.
• So the fraction becomes 3^25 / 3^24 = 3 × 3^24 / 3^24 = 3.