SAT Math

Category - Algebra and Functions

Calculate (8^3 × 16^6)/4^15 .
  1. 1
  2. 2
  3. 4
  4. 8
  5. 16
Explanation
Answer: D - The value of the expression is 8. Use a^x × a^y = a^(x + y), a^x/a^y = a^(x − y) and (a^x )^y = a^xy. The common base for 4, 8, and 16 is 2.
(8^3 × 16^6)/4^15 = ((2^3)^3 × (2^4)^6)/(2^2)^15 = (2^9 × 2^24)/2^30 = 2^(9 + 24)/2^30 = 2^33/2^30 = 2^(33 − 30) = 2^3 = 8
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