which equation is equivalent to $2^{4x}=8^{x - 3}$?\n$2^{4x}=2^{2x - 3}$\n$2^{4x}=2^{2x - 6}$\n$2^{4x}=2^{3x…

which equation is equivalent to $2^{4x}=8^{x - 3}$?\n$2^{4x}=2^{2x - 3}$\n$2^{4x}=2^{2x - 6}$\n$2^{4x}=2^{3x - 3}$\n$2^{4x}=2^{3x - 9}$

which equation is equivalent to $2^{4x}=8^{x - 3}$?\n$2^{4x}=2^{2x - 3}$\n$2^{4x}=2^{2x - 6}$\n$2^{4x}=2^{3x - 3}$\n$2^{4x}=2^{3x - 9}$

Answer

Explanation:

Step1: Rewrite 8 as a power of 2

Since $8 = 2^3$, then $8^{x - 3}=(2^3)^{x - 3}$.

Step2: Apply power - of - a - power rule

According to the power - of - a - power rule $(a^m)^n=a^{mn}$, so $(2^3)^{x - 3}=2^{3(x - 3)}$. Expand $3(x - 3)$: $3(x - 3)=3x-9$. So $8^{x - 3}=2^{3x - 9}$, and the equation $2^{4x}=8^{x - 3}$ is equivalent to $2^{4x}=2^{3x - 9}$.

Answer:

$2^{4x}=2^{3x - 9}$ (the last option)