EXAMPLES:
Question:
Write
$\,(3x)(x)^4\,$ in the form $\,kx^n\,$.
Solution:
$\,3x^5\,$
Why? Keep reading!
Here's the strategy:

Make three passes through the expression,
figuring out the SIGN, SIZE, and VARIABLE PART.

On the first pass, just figure out the plus/minus sign.
There are five factors of $\,1\,$ (one outside, four inside);
this is an odd number, so the result is negative.
Here are those five factors:
$\,\overset{\downarrow}{}(3x)(\overset{\downarrow}{}x)^{\overset{\downarrow}{4}}\,$

On the second pass, figure out the size of the answer;
you're ignoring all the plus/minus signs, because you took care of them on the first pass.
The size is $\,3\,$:
$\,(\overset{\downarrow}{3}x)(x)^4\,$

On the third pass, figure out the power of $\,x\,$.
There are five factors of $\,x\,$, so the variable part is $\,x^5\,$:
$\,(3\overset{\downarrow}{x})(\overset{\downarrow}{x})^{\overset{\downarrow}{4}}\,$
 Put it all together to get $\,3x^5\,$.
Question:
Write
$\,(1)^2(3x)^2(x)^2\,$ in the form $\,kx^n\,$.
Solution:
$\,9x^4\,$

Sign:
There are six factors of $\,1\,$;
this is an even number, so the result is positive:
$\,(\overset{\downarrow}{}1)^{\overset{\downarrow}{2}}
(\overset{\downarrow}{}3)^{\overset{\downarrow}{2}}
(\overset{\downarrow}{}x)^{\overset{\downarrow}{2}}
\,$

Size:
The size is $\,9\,$:
$\,(1)^2(\overset{\downarrow}{3}x)^{\overset{\downarrow}{2}}(x)^2\,$

Variable part:
There are four factors of $\,x\,$, so the variable part is $\,x^4\,$:
$\,(1)^2
(3\overset{\downarrow}{x})^{\overset{\downarrow}{2}}
(\overset{\downarrow}{x})^{\overset{\downarrow}{2}}
\,$
 Put it all together to get $\,9x^4\,$.
Question:
Write
$\,(1)^4(x^3)(2x)(x^2)\,$ in the form $\,kx^n\,$.
Solution:
$\,2x^6\,$

Sign:
There are seven factors of $\,1\,$;
this is an odd number, so the result is negative:
$\,(\overset{\downarrow}{}1)^{\overset{\downarrow}{4}}
(\overset{\downarrow}{}x^3)
(\overset{\downarrow}{}2x)
(\overset{\downarrow}{}x^2)
\,$

Size:
The size is $\,2\,$:
$\,(1)^4(x^3)(\overset{\downarrow}{2}x)(x^2)\,$

Variable part:
There are six factors of $\,x\,$, so the variable part is $\,x^6\,$:
$\,(1)^4
(\overset{\downarrow}{x}{}^{\overset{\downarrow}{3}})
(2\overset{\downarrow}{x})
(\overset{\downarrow}{x}{}^{\overset{\downarrow}{2}})\,$
 Put it all together to get $\,2x^6\,$.
Helpful facts to remember:
$2^5 = 32$
$3^4 = 81$
$3^5 = 243$
$4^3 = 64$
$5^3 = 125$