GreenlightTestPrep wrote:
\(\sqrt{4^{15} + 4^{15} + 4^{15} + 4^{15}} =\)
(A) \(2^8\)
(B) \(2^{15}\)
(C) \(2^{16}\)
(D) \(2^{30}\)
(E) \(2^{32}\)
Using the properties of Exponents:
\(x^ax^b = x^{a+b}\) and \((x^a)^b = x^{ab}\)
\(4^{15} + 4^{15} + 4^{15} + 4^{15} = 4(4^{15}) = 2^2[2^{(2)(15)}] = 2^2(2^{30}) = 2^{2+30} = 2^32\)
Now, \(\sqrt{2^32} = 2^{16}\)
Hence, option C
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I hope this helps!
Regards:
Karun Mendiratta
Founder and Quant Trainer
Prepster Education, Delhi, Indiahttps://www.instagram.com/prepster_education/