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

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!
• PRACTICE (online exercises and printable worksheets
Want more details, more exercises?

EXAMPLES:
Question: Write $\,(3x)^2\,$ 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 $\,(2x)^3\,$ 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 $\,(-3x)^2\,$ 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:
• it's a negative number to an even power; so, the answer will be positive
• 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:
$(-2x)^3 = (-2)^3x^3 = -8x^3\,$
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:
• it's a negative number to an odd power; so, the answer will be negative
• What's the size of the answer?   $2^3 = 8$
• What's the variable part?   $x^3$
• put it together to get $\,-8x^3$

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

Master the ideas from this section
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 $\,kx^n$ :