WRITING MORE COMPLICATED EXPRESSIONS IN THE FORM $\,kx^n\,$
EXAMPLES:
Question: Write [beautiful math coming... please be patient] $\,-(3x)^2\,$ in the form $\,kx^n\,$.
Solution:
[beautiful math coming... please be patient] $-(3x)^2 = (-1)3^2x^2 = -9x^2\,$
or
[beautiful math coming... please be patient] $-(3x)^2 = (-1)(3x)(3x) = (-1)(3\cdot 3)(x\cdot x) = -9x^2$
Question: Write [beautiful math coming... please be patient] $\,-(2x)^3\,$ in the form $\,kx^n\,$.
Solution:
[beautiful math coming... please be patient] $-(2x)^3 = (-1)2^3x^3 = -8x^3\,$
or
[beautiful math coming... please be patient] $-(2x)^3 = (-1)(2x)(2x)(2x) = (-1)(2\cdot 2\cdot 2)(x\cdot x\cdot x) = -8x^3$
Question: Write [beautiful math coming... please be patient] $\,-(-3x)^2\,$ in the form $\,kx^n\,$.
Solution:
[beautiful math coming... please be patient] $-(-3x)^2 = (-1)(-3)^2x^2 = -9x^2\,$
or
[beautiful math coming... please be patient] $-(-3x)^2 = (-1)(-3x)(-3x) = (-1)(-3\cdot -3)(x\cdot x) = -9x^2$

For mental math, the following thought process can be used:
Question: Write [beautiful math coming... please be patient] $\,-(-2x)^3\,$ in the form $\,kx^n\,$.
Solution:
[beautiful math coming... please be patient] $-(-2x)^3 = (-1)(-2)^3x^3 = 8x^3\,$
or
[beautiful math coming... please be patient] $-(-2x)^3 = (-1)(-2x)(-2x)(-2x) = (-1)(-2\cdot -2\cdot -2)(x\cdot x\cdot x) = 8x^3$

For mental math, the following thought process can be used:

Helpful facts to remember:

$2^5 = 32$             $3^4 = 81$             $3^5 = 243$             $4^3 = 64$             $5^3 = 125$

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Writing Quite Complicated Expressions in the form $\,kx^n$

 
 

Input the exponent using the   “ ^ ”   key:   on my keyboard, it is above the $\,6\,$.

Write  
  in the form [beautiful math coming... please be patient] $\,kx^n$ :
    
(MAX is 11; there are 11 different problem types.)