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Negative Exponents

Negative Exponents. 5 ¯². Negative number raised to a positive even power. If a negative number is raised to a “positive even” power, the answer or result will be a positive number. (-5) ⁴ = (-5)(-5)(-5)(-5) = 625 Note that the number is negative , not the exponent.

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Negative Exponents

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  1. Negative Exponents 5¯²

  2. Negative number raised to a positive even power If a negative number is raised to a “positive even” power, the answer or result will be a positive number. (-5)⁴ = (-5)(-5)(-5)(-5) = 625 Note that the number is negative, not the exponent. Note that the exponent is positive. Remember that a negative number with a positive exponent will give a positive number or answer. neg neg pos pos pos

  3. Negativenumber raised to a positive odd power If a negative number is raised to a positive, but odd power, the results or answer will be negative. (-4)³ = (-4)³(-4)³(-4)³ = -64 Understand that as you multiply, you start of negative, then you multiply again and its positive, one more time yields a negative number. neg neg pos neg

  4. + /- number raised to a negative power If a positive or negative number is raised to a negative power, it can be equally written, one over that number raised to the positive power. The positive number – positive to negative exponent. 3¯³ = 1/ 3³ The negative number – negative to negative exponent. (-3)¯³ = 1/ (-3)³ = 1/ (-3) x 1/ (-3) x 1/ (-3) = 1/-27 (ooopps!!! Remember the rule on page three – (If a negative number is raised to a positive, but odd power, the results or answer will be negative.) Simply, just write 1 over the number and drop the negative sign on the exponent!

  5. Negative Exponent and the Quotient Rule When dividing a polynomial with exponents, we use the quotient rule, which sometimes may leave a negative exponential answer. One quick way to determine if you are going to have a negative exponent in your answer, is to determine whether the exponent in the denominator is larger than the exponent in the numerator. For example: The quotient rule The quotient rule says to perform your division , then subtract the exponent of the denominator from the exponent of the numerator. The Negative exponent rule says to write one over the term with the negative exponent and drop the negative sign.

  6. Lets look at some more… We just flipped it! Let s say that a negative exponent is just on the wrong side of the fraction line! So we just flip it, then the negative sign is gone! We could also say “take the reciprocal of…”. Negative exponent in the denominator. A monomial with a negative power. Raising to a negative power. Remember that you are only taking the reciprocal of the term with the negative exponent. When you flip it you will find that now you have to apply the product rule, that is aⁿ • aⁿ = aⁿ⁺ⁿ In this example, there is a term with a coefficient and a variable to a negative power of one. The negative power is on the variable, not on the coefficient. Therefore, take the reciprocal of the variable and negative power. The 3 does not move with the variable because the negative power is only on the variable. Raise each term inside of the parenthesis to the negative power. Now flip or take the reciprocal and drop the negative signs. Factor out 3² and x² to (3)(3) = 9, and (x)(x) = x². Now you have 1 x1 = 1 over 9 • x² = 9x².

  7. Last one… Make sure you understand this… You need to raise the numerator and the denominator to the negative power. Following the example, remember to keep the parenthesis. You will notice that y and z both have negative exponents. You want to raise the variable along with its negative exponent to the negative power on the outside of the whole set. Now you must apply the power rule to the numerator and to the denominator. The power rule states that when you raise an exponential expression (the term already has an exponent) to a power, you multiply the exponents. Remember your rules for negative signs. (-)(-) = (+) Or if you good, you can do the flip thing. Once you have raised the terms to the power, take the reciprocal and drop the negative sign of the power on the outside of the parenthesis. Remember the power on the inside of the parenthesis belongs to the variable. Now apply the product rule. Ooopps! I still have negative exponents on my variables! The negative exponent rule says “flip”, and drop the negative sign!. That’s it. You’re done! Lol!

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