NEGATIVE EXPONENTS

27/9 = 3 or 27/9 = 3³/3² = 3^3-2 = 3 The exponent for 3 is a positive “1” but we don’t write it. It is understood to be there.

9/27 reduces to 1/3. Using exponents 9/27 = 3²/3³ = 3^2-3 = 3^-1 = 1/3 We subtract exponents when we divide and this process must give us the same answer 1/3 or else the process is wrong. We learn from this that if you have an answer with a negative exponent then you put it in the denominator and the exponent becomes positive. Try the following probems:

1. a⁴/a⁷ = answer

2. Z⁶/Z¹⁵ = answer

3. m^-7/m-⁵ = answer

 Multiplication of negative exponents has to follow the same rules as those for positive exponents. 

Therefore t^-3 x t^-4 = t ^{-3 + (-4)} = t^-7  which equals 1/t⁷  Try the following problems:

1.   r ^-7 x r ^-3 =  answer

2.   p ^-5 p ⁴  =   answer

3.   w ^{- 6}  w ⁶ =  answer

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