Once you"ve learned about an unfavorable numbers, you can additionally learn about an unfavorable powers. A an unfavorable exponent just method that the basic is top top the wrong side of the portion line, so you have to flip the basic to the various other side. For instance, "x–2" (pronounced as "ecks come the minus two") just means "x2, however underneath, as in 1/(x2)".

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create x–4 using only positive exponents.

I understand that the negative exponent means that the base, the x, belongs on the other side of the portion line. Yet there isn"t a fraction line!


To deal with this, I"ll an initial convert the expression into a fraction in the method that any expression deserve to be converted into a fraction: by placing it over "1". Of course, once I move the base to the various other side that the fraction line, there will certainly be naught left ~ above top. But since anything can also be related to as gift multiplied through 1, I"ll leave a 1 ~ above top.

Here"s what that looks like:


Once ns no longer needed the "1" under (to create the fraction), ns omitted it, because I had the variable expression underneath, and also the "times one" doesn"t adjust anything.

compose x2 / x–3 using only positive exponents.

Only one of the terms has actually a an unfavorable exponent. This means that I"ll only be moving one of these terms. The term through the an adverse power is underneath; this means that I"ll be moving it increase top, to the various other side that the fraction line. There currently is a hatchet on top; I"ll be using exponent rules to combine these 2 terms.

Once I move that denominator up top, ns won"t having actually anything left under (other 보다 the "understood" 1), so I"ll drop the denominator.


The an unfavorable power will come to be just "1" when I move the basic to the various other side the the portion line. Anything to the power 1 is simply itself, therefore I"ll be able to drop this power as soon as I"ve relocated the base.


Make sure you understand why the "2" above does not relocate with the variable: the an unfavorable exponent is just on the "x", so just the x moves..

I"ve obtained a number inside the strength this time, and a variable, for this reason I"ll have to remember to simplify the numerical squaring.

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Unlike the previous exercise, the parentheses intended that the negative power go indeed use to the three and also the variable.

compose (-5x-1)/(y3) using only positive powers.

The "minus one" strength on the x method that I"ll require to move that x to the various other side of the fraction line. But the "minus" ~ above the 5 way only the the 5 is negative. This "minus" is not a power, so it doesn"t to speak anything around moving the 5 anywhere!