Question

question 3 (mandatory) (1 point)
27^{2x} expressed as a power of 3 is
a) 3^{3 + 2x}
b) 3^{8x}
c) 3^{9x}
d) 3^{6x}

Explanation:

Step1: Rewrite 27 as a power of 3

Since \(27 = 3^3\), then \(27^{2x}=(3^3)^{2x}\).

Step2: Apply power - of - a - power rule

The power - of - a - power rule \((a^m)^n=a^{mn}\). Here \(a = 3\), \(m = 3\) and \(n = 2x\), so \((3^3)^{2x}=3^{3\times2x}=3^{6x}\).

Answer:

d) \(3^{6x}\)