# Recognizing the patterns $\,x^n\,$ and $\,(-x)^n$

You may want to explore these related concepts first: Equal or Opposites?

## 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.