Write in simplest form. Explain your work.72^(-4)+3(-4)                                                                  

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

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The simplified form of the expression `72^(-4) + 3(-4)` is required.

`72^(-4) + 3(-4)`

`72^(-4) = 1/72^4` and `3*(-4) = -12`

=> `1/72^4 - 12`

=> `(1 - 12*72^4)/72^4`

The simplified form of the expression `72^(-4) + 3(-4) = (1 - 12*72^4)/72^4`

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

Supposing that you need to evaluate `72^(-4) + 3^(-4), ` you need to remember that `72 = 8*9,`  hence `72^(-4) = (8*9)^(-4)`

You need to write `9 = 3^2 =gt 9^(-4) = (3^2)^(-4) = 3^(2*(-4))`

`9^(-4) = 3^(-8)`

`72^(-4) + 3^(-4) = 8^(-4)*3^(-8) + 3^(-4) `

`72^(-4) + 3^(-4) = 3^(-4)*(8^(-4)*3^(-4) + 1)`

You need to remember that the negative power is the reverse of positive power such that:

`72^(-4) + 3^(-4) = 1/(3^4)*(1/((8*3)^4) + 1)`

`72^(-4) + 3^(-4) = 1/(3^4)*(24^4 + 1)/(24^4)`

`72^(-4) + 3^(-4) = (24^4 + 1)/(72^4)`

Hence, evaluating the addition of negative powers yields `72^(-4) + 3^(-4) = (24^4 + 1)/(72^4).`

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