Question

1. $4^x + 12^x =$

a $4^x(1 + 3^x)$
b $4(5^x)$
c $16^x$
d $16^{2x}$

Explanation:

Step1: Factor out the common term

Notice that \(12^x = (4\times3)^x = 4^x\times3^x\) (using the property \((ab)^x = a^x b^x\)). So we can factor out \(4^x\) from \(4^x + 12^x\).
\(4^x + 12^x = 4^x + 4^x\times3^x\)

Step2: Apply the distributive property

Using the distributive property \(ab + ac = a(b + c)\), where \(a = 4^x\), \(b = 1\), and \(c = 3^x\), we get:
\(4^x(1 + 3^x)\)

Answer:

A. \(4^x(1 + 3^x)\)