Recognizing the patterns x^n and (-x)^n

EXAMPLES:

In the exercise, you will be filling in the blanks:

The expression

$\,(-y)^{24}\,$ is of the form

$\,(-x)^n\,$
where $\,x\,$ is and $\,n\,$ is .

Note that in the pattern

$\,(-x)^n\,$,
the variable ‘$\,x\,$’ represents whatever comes after the minus sign,
and the variable ‘$\,n\,$’ represents the exponent.

The expression

$\,(-3x)^{13}\,$ is of the form

$\,(-x)^n\,$
where $\,x\,$ is and $\,n\,$ is .

Try not to be confused by the appearance of the variable ‘$\,x\,$’ in two places!
Again, we're matching something to the pattern

$\,(-x)^n\,$,
where ‘$\,x\,$’ represents whatever comes after the minus sign.
What comes after the minus sign in $\,(-3x)^{13}\,$?
Answer: $\,3x\,$

The expression

$\,(-2x)^{7}\,$ is of the form

$\,x^n\,$
where $\,x\,$ is and $\,n\,$ is .

Here, we're matching something to the pattern

$\,x^n\,$,
so ‘$\,x\,$’ represents the entire base.

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 Expressions in the form $\,kx^n$