Which of the following is correct ? A) 1/4(2n) = 2n - 2B) 4n - 1 = 4n

1.	Which of the following is correct ? A) 1/4(2n) = 2n - 2B) 4n - 1 = 4nC) 4m × 4-m = 4-2m D) 25 (5n) = 5n - 1
Answer» Correct option is (A) 1/4 (2ⁿ) = 2^n-2 (A) \(\frac{1}{4}(2^n)=\frac{2^n}{2^2}=2^{n-2}\) (Correct) (B) \(4^{n-1}=4^n\times4^{-1}=\frac{4^n}4\) (Incorrect) (C) \(4^m\times4^{-m}=4^{m+(-m)}=4^{m-m}=4^0=1\neq4^{-2m}\) (Incorrect) (D) \(25\,(5^n)=5^2\times5^n=5^{2+n}\neq5^{n-1}\) (Incorrect) A) 1/4(2ⁿ) = 2^{n - 2}

Which of the following is correct ? A) 1/4(2n) = 2n - 2B) 4n - 1 = 4nC) 4m × 4-m = 4-2m D) 25 (5n) = 5n - 1

Answer»

Correct option is (A) 1/4 (2ⁿ) = 2^n-2

(A) \(\frac{1}{4}(2^n)=\frac{2^n}{2^2}=2^{n-2}\) (Correct)

(B) \(4^{n-1}=4^n\times4^{-1}=\frac{4^n}4\) (Incorrect)

(D) \(25\,(5^n)=5^2\times5^n=5^{2+n}\neq5^{n-1}\) (Incorrect)

A) 1/4(2ⁿ) = 2^{n - 2}