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

You are watching: What is 5 to the negative 2 power

*x*–4 using only positive exponents.

I recognize that the negative exponent method that the base, the *x*, belong on the various other side the the fraction line. Yet there isn"t a portion line!

To deal with this, I"ll 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 move the basic to the various other side of the fraction line, there will be naught left top top top. But due to the fact that anything can likewise be pertained to as gift multiplied by 1, I"ll leaving a 1 on top.

Here"s what that looks like:

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

write*x*2 /

*x*–3 using only positive exponents.

Only one of the terms has a negative exponent. This way that I"ll only be relocating one of this terms. The term through the an adverse power is underneath; this method that I"ll be relocating it up top, to the various other side that the portion line. There already is a ax on top; I"ll be using exponent rules to incorporate these 2 terms.

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

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

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

I"ve acquired a number inside the strength this time, and a variable, so I"ll need to remember to simplify the number squaring.

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Unlike the ahead exercise, the parentheses supposed that the an unfavorable power did indeed use to the three and the variable.

compose (-5*x*-1)/(

*y*3) using only positive powers.

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