﻿ Writing More Complicated Expressions in the Form kx^n
WRITING MORE COMPLICATED EXPRESSIONS IN THE FORM $\,kx^n\,$

EXAMPLES:
Question: Write $\,-(3x)^2\,$ in the form $\,kx^n\,$.
Solution:
$-(3x)^2 = (-1)3^2x^2 = -9x^2\,$
or
$-(3x)^2 = (-1)(3x)(3x) = (-1)(3\cdot 3)(x\cdot x) = -9x^2$
Question: Write $\,-(2x)^3\,$ in the form $\,kx^n\,$.
Solution:
$-(2x)^3 = (-1)2^3x^3 = -8x^3\,$
or
$-(2x)^3 = (-1)(2x)(2x)(2x) = (-1)(2\cdot 2\cdot 2)(x\cdot x\cdot x) = -8x^3$
Question: Write $\,-(-3x)^2\,$ in the form $\,kx^n\,$.
Solution:
$-(-3x)^2 = (-1)(-3)^2x^2 = -9x^2\,$
or
$-(-3x)^2 = (-1)(-3x)(-3x) = (-1)(-3\cdot -3)(x\cdot x) = -9x^2$

For mental math, the following thought process can be used:
• How many factors of $-1$ are there? Three (one outside, two inside); this is an odd number, so the answer is negative
• 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:
$-(-2x)^3 = (-1)(-2)^3x^3 = 8x^3\,$
or
$-(-2x)^3 = (-1)(-2x)(-2x)(-2x) = (-1)(-2\cdot -2\cdot -2)(x\cdot x\cdot x) = 8x^3$

For mental math, the following thought process can be used:
• How many factors of $-1$ are there? Four (one outside, three inside); this is an even number, so the answer is positive
• 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 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 $\,kx^n$ :