EXAMPLES:
Question:
Write
$\,(3x)^2\,$ in the form $\,kx^n\,$.
Solution:
$(3x)^2 = (1)3^2x^2 = 9x^2\,$
or
$(3x)^2 = (1)(3x)(3x) = (1)(3\cdot 3)(x\cdot x) = 9x^2$
Question:
Write
$\,(2x)^3\,$ in the form $\,kx^n\,$.
Solution:
$(2x)^3 = (1)2^3x^3 = 8x^3\,$
or
$(2x)^3 = (1)(2x)(2x)(2x) = (1)(2\cdot 2\cdot 2)(x\cdot x\cdot x) = 8x^3$
Question:
Write
$\,(3x)^2\,$ in the form $\,kx^n\,$.
Solution:
$(3x)^2 = (1)(3)^2x^2 = 9x^2\,$
or
$(3x)^2 = (1)(3x)(3x) = (1)(3\cdot 3)(x\cdot x) = 9x^2$
For mental math, the following thought process can be used:

How many factors of $1$ are there?
Three (one outside, two inside);
this is an odd number, so the answer is negative

What's the size of the answer?
$3^2 = 9$

What's the variable part?
$x^2$

put it together to get $\,9x^2$
Question:
Write
$\,(2x)^3\,$ in the form $\,kx^n\,$.
Solution:
$(2x)^3 = (1)(2)^3x^3 = 8x^3\,$
or
$(2x)^3 = (1)(2x)(2x)(2x) = (1)(2\cdot 2\cdot 2)(x\cdot x\cdot x) = 8x^3$
For mental math, the following thought process can be used:

How many factors of $1$ are there?
Four (one outside, three inside); this is an even number, so the answer is positive

What's the size of the answer?
$2^3 = 8$

What's the variable part?
$x^3$

put it together to get $\,8x^3$
Helpful facts to remember:
$2^5 = 32$
$3^4 = 81$
$3^5 = 243$
$4^3 = 64$
$5^3 = 125$