Once you"ve learned about an adverse numbers, girlfriend can also learn about negative powers. A an adverse exponent just way that the base is ~ above the wrong next of the fraction line, so you must flip the base to the other side. For instance, "x–2" (pronounced as "ecks to the minus two") just method "x2, but underneath, as in 1/(x2)".

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compose x–4 using just positive exponents.

I recognize that the an unfavorable exponent way that the base, the x, belongs on the various other side of the fraction line. However there isn"t a portion line!


To deal with this, I"ll very first convert the expression right into a fraction in the means that any expression can be converted into a fraction: by putting it end "1". Of course, when I relocate the basic to the other side the the portion line, there will certainly be nothing left ~ above top. But because anything can likewise be concerned as gift multiplied by 1, I"ll leave a 1 ~ above top.

Here"s what it looks like:


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

write x2 / x–3 using just positive exponents.

Only one of the terms has a negative exponent. This way that I"ll just be moving one of these terms. The term through the an adverse power is underneath; this means that I"ll be moving it up top, to the other side that the portion line. There currently is a ax on top; I"ll be making use of exponent rules to combine these two terms.

Once I relocate that denominator increase top, i won"t having actually anything left under (other 보다 the "understood" 1), for this reason I"ll drop the denominator.


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


Make sure you know why the "2" over does not relocate with the variable: the negative exponent is just on the "x", so only the x moves..

I"ve gained a number within the strength this time, as well as a variable, so I"ll need to remember to simplify the number squaring.

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

create (-5x-1)/(y3) using just positive powers.

The "minus one" strength on the x means that I"ll need to move that x come the other side of the portion line. But the "minus" ~ above the 5 means only that the 5 is negative. This "minus" is not a power, so it doesn"t say anything about moving the 5 anywhere!