Writing Quite Complicated Expressions in the Form $kx^n$
Want some very basic practice first? Writing Expressions in the Form $\,kx^n\,$
Here's some mediumdifficulty practice: Writing More Complicated Expressions in the Form $\,kx^n\,$
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:
$$\cssId{s25}{\overset{\downarrow}{}}(3x) \cssId{s26}{(\overset{\downarrow}{}x)^{\overset{\downarrow}{4}}}$$ 
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 $\,3\,$:
$$(\cssId{s30}{\overset{\downarrow}{3}}x)(x)^4$$ 
On the third pass, figure out the power of $\,x\,.$ There are five factors of $\,x\,$, so the variable part is $\,x^5\,$:
$$(3\cssId{s33}{\overset{\downarrow}{x}})\cssId{s34}{(\overset{\downarrow}{x})^{\overset{\downarrow}{4}}}$$  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:
$$ \cssId{s43}{(\overset{\downarrow}{}1)^{\overset{\downarrow}{2}}} \cssId{s44}{(\overset{\downarrow}{}3)^{\overset{\downarrow}{2}}} \cssId{s45}{(\overset{\downarrow}{}x)^{\overset{\downarrow}{2}}} $$ 
Size: The size is $\,9\,$:
$$(1)^2 \cssId{s48}{(\overset{\downarrow}{3}x)^{\overset{\downarrow}{2}}}(x)^2$$ 
Variable part: There are four factors of $\,x\,,$ so the variable part is $\,x^4\,$:
$$(1)^2 \cssId{s51}{(3\overset{\downarrow}{x})^{\overset{\downarrow}{2}}} \cssId{s52}{(\overset{\downarrow}{x})^{\overset{\downarrow}{2}}} $$  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:
$$ \cssId{s61}{(\overset{\downarrow}{}1)^{\overset{\downarrow}{4}}} \cssId{s62}{(\overset{\downarrow}{}x^3)} \cssId{s63}{(\overset{\downarrow}{}2x)} \cssId{s64}{(\overset{\downarrow}{}x^2)} $$ 
Size: The size is $\,2\,$:
$$(1)^4(x^3) \cssId{s67}{(\overset{\downarrow}{2}x)}(x^2)$$ 
Variable part: There are six factors of $\,x\,,$ so the variable part is $\,x^6\,$:
$$(1)^4 \cssId{s70}{(\overset{\downarrow}{x}{}^{\overset{\downarrow}{3}})} \cssId{s71}{(2\overset{\downarrow}{x})} \cssId{s72}{(\overset{\downarrow}{x}{}^{\overset{\downarrow}{2}})}$$  Put it all together to get $\,2x^6\,.$
Helpful facts to remember:
$$\cssId{s75}{2^5 = 32}$$ $$\cssId{s76}{3^4 = 81}$$ $$\cssId{s77}{3^5 = 243}$$ $$\cssId{s78}{4^3 = 64}$$ $$\cssId{s79}{5^3 = 125}$$Practice
Input the exponent using the ‘ ^ ’ key: on my keyboard, it is above the $\,6\,$.

If the answer is (say) $\,3\,$, you must write it as:
3x^0

If the answer is (say) $\,3x\,$, you must write it as:
3x^1