WRITING EXPRESSIONS IN THE FORM $\,kx^n\,$

LESSON READ-THROUGH
by Dr. Carol JVF Burns (website creator)
Follow along with the highlighted text while you listen!
Note:
When you're looking at the math, then:
$\,(3x)^2\,$ is most easily read aloud as: ‘three ex, (slight pause), squared’
$\,3x^2\,$ is most easily read aloud as: ‘three, (very slight pause), ex squared’
In this lesson, some pauses are over-emphasized to help you hear them!
 
EXAMPLES:
Question: Write [beautiful math coming... please be patient] $\,(3x)^2\,$ in the form $\,kx^n\,$.
Solution:
$(3x)^2 = 3^2x^2 = 9x^2\,$
or
$(3x)^2 = (3x)(3x) = (3\cdot 3)(x\cdot x) = 9x^2$
Question: Write [beautiful math coming... please be patient] $\,(2x)^3\,$ in the form $\,kx^n\,$.
Solution:
$(2x)^3 = 2^3x^3 = 8x^3\,$
or
$(2x)^3 = (2x)(2x)(2x) = (2\cdot 2\cdot 2)(x\cdot x\cdot x) = 8x^3$
Question: Write [beautiful math coming... please be patient] $\,(-3x)^2\,$ in the form $\,kx^n\,$.
Solution:
$(-3x)^2 = (-3)^2x^2 = 9x^2\,$
or
$(-3x)^2 = (-3x)(-3x) = (-3\cdot -3)(x\cdot x) = 9x^2$

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:
$(-2x)^3 = (-2)^3x^3 = -8x^3\,$
or
$(-2x)^3 = (-2x)(-2x)(-2x) = (-2\cdot -2\cdot -2)(x\cdot x\cdot x) = -8x^3$

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 More 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.)