Writing More Complicated Expressions in the Form kx^n

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Want some simpler practice first? Writing Expressions in the Form $\,kx^n\,$
Ready to move on to more difficult problems? Writing Quite 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 $\,8x^3$

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 $\,6\,$.

(MAX is 11; there are 11 different problem types.)