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Once you"ve learned about negative numbers, you have the right to likewise learn about negative powers. A negative exponent simply suggests that the base is on the wrong side 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") simply means "x2, yet underneath, as in 1/(x2)".

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

Write x–4 making use of only positive exponents.

I understand that the negative exponent implies that the base, the x, belongs on the other side of the fractivity line. But tright here isn"t a portion line!


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To solve this, I"ll first transform the expression right into a portion in the method that any expression deserve to be converted into a fraction: by putting it over "1". Of course, as soon as I move the base to the various other side of the fractivity line, tbelow will certainly be nopoint left on peak. But since anything have the right to additionally be concerned as being multiplied by 1, I"ll leave a 1 on optimal.

Here"s what it looks like:


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Once I no much longer required the "1" underneath (to create the fraction), I omitted it, bereason I had the variable expression underneath, and also the "times one" doesn"t readjust anything.

Write x2 / x–3 making use of just positive exponents.

Only among the terms has an unfavorable exponent. This indicates that I"ll only be moving among these terms. The term with the negative power is underneath; this means that I"ll be relocating it up height, to the various other side of the fraction line. Tright here already is a term on top; I"ll be using exponent rules to incorporate these two terms.

Once I relocate that denominator up height, I won"t having anything left underneath (various other than the "understood" 1), so I"ll drop the denominator.


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The negative power will certainly end up being just "1" as soon as I relocate the base to the various other side of the fraction line. Anypoint to the power 1 is just itself, so I"ll have the ability to drop this power once I"ve moved the base.


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Make sure you understand 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 obtained a number inside the power this time, as well as a variable, so I"ll need to remember to simplify the numerical squaring.

See more: The Distance Along A Circle Between Two Points On The Circle S


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Unfavor the previous exercise, the parentheses supposed that the negative power did indeed use to the three and also the variable.

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

The "minus one" power on the x indicates that I"ll need to move that x to the other side of the fraction line. But the "minus" on the 5 indicates only that the 5 is negative. This "minus" is not a power, so it doesn"t say anything around moving the 5 anywhere!