Writing Expressions in the Form kx^n

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:

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:

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 $\,6\,$.

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