which equation is equivalent to $4^{x + 3}=64$?\n$2^{x + 6}=2^{4}$\n$2^{2x + 6}=2^{6}$\n$4^{2x +…
which equation is equivalent to $4^{x + 3}=64$?\n$2^{x + 6}=2^{4}$\n$2^{2x + 6}=2^{6}$\n$4^{2x + 6}=4^{2}$\n$4^{x + 3}=4^{6}$
Answer
Explanation:
Step1: Rewrite bases as powers of 2
Since (4 = 2^2) and (64=2^6), the equation (4^{x + 3}=64) can be rewritten as ((2^2)^{x + 3}=2^6).
Step2: Apply power - of - a - power rule
By the power - of - a - power rule ((a^m)^n=a^{mn}), ((2^2)^{x + 3}=2^{2(x + 3)}=2^{2x+6}). So the equation becomes (2^{2x + 6}=2^6).
Answer:
B. (2^{2x + 6}=2^6)