Carcass wrote:
Which if the following equal \((8)(72)^{-5}\)
A. \(8^{-4}\)
B. \(8^{-5}\)
C. \(\frac{(72)^{-4}}{9}\)
D. \(\frac{(72)^{-5}}{8}\)
E. \(\frac{(72)^{-6}}{9}\)
Kudos for the right answer and solution.
Useful property: \((xy)^n = (x^n)(y^n)\)Given: \((8)(72)^{-5}\)
Rewrite 72 as (8)(9) to get: \((8^1)(8^{-5})(9^{-5})\)
Simplify: \((8^{-4})(9^{-5})\)
Rewrite \(9^{-5}\) as follows: \((8^{-4})(9^{-4})(9^{-1})\)
Combine first two expressions: \((72^{-4})(9^{-1})\)
Rewrite \(9^{-1}\) as fraction to get: \((72^{-4})(\frac{1}{9})\)
Simplify: \(\frac{72^{-4}}{9}\)
Answer: C
Cheers,
Brent