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Once you"ve learned about negative numbers, you can additionally learn about an adverse powers. A an unfavorable exponent just way that the base is ~ above the wrong side of the fraction line, for this reason you should flip the base to the various other side. Because that instance, "x–2" (pronounced as "ecks come the minus two") just means "x2, but underneath, together in 1/(x2)".

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create x–4 using only positive exponents.

I recognize that the an unfavorable exponent method that the base, the x, belong on the other side that the portion line. However there isn"t a portion line!

To settle this, I"ll very first convert the expression right into a fraction in the method that any expression can be converted right into a fraction: by putting it end "1". That course, once I relocate the base to the other side the the fraction line, there will certainly be naught left on top. But since anything can likewise be concerned as being multiplied by 1, I"ll leaving a 1 ~ above top.

Here"s what the looks like:

Once i no much longer needed the "1" under (to develop the fraction), i omitted it, since I had the change 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 a negative exponent. This means that I"ll just be moving one of these terms. The term with the an unfavorable power is underneath; this method that I"ll be relocating it increase top, to the other side that the fraction line. There currently is a term on top; I"ll be utilizing exponent rule to incorporate these 2 terms.

Once I move that denominator up top, ns won"t having actually anything left underneath (other 보다 the "understood" 1), for this reason I"ll fall the denominator.

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

Make sure you understand why the "2" over does not move with the variable: the an unfavorable exponent is only on the "x", so only the x moves..

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

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Unlike the vault exercise, the parentheses expected that the an adverse power walk indeed use to the three and the variable.

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

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