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Simplify: Read the explanation box before answering since it might confuse you. 24a^-2...

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bookworm309 | Student, Grade 9 | eNoter

Posted October 29, 2012 at 1:46 PM via web

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Simplify:

Read the explanation box before answering since it might confuse you.

24a^-2 times b^3

divided by

12a^4 times b^-2 

The divided by part is supposed be a division bar with the top being the numerator and the bottom being the demoninator.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted October 29, 2012 at 2:06 PM (Answer #1)

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You need to simplify the following expression such that:

`(24*a^(-2)*b^3)/(12a^4*(b^-2))`

You need to use negative power property such that:

`a^(-2) = 1/a^2`

`b^(-2) = 1/b^2`

`(24*b^3/a^2)/(12a^4/b^2) = (24/12)(b^3/a^2)*(b^2/a^4)`

Using exponential identities yields:

`(24*a^(-2)*b^3)/(12a^4*(b^-2)) = 2*(b^(3+2))/(a^(2+4))`

`(24*a^(-2)*b^3)/(12a^4*(b^-2)) = 2b^5/a^6 = 2a^(-6)b^5`

Hence, simplifying the given expression yields `(24*a^(-2)*b^3)/(12a^4*(b^-2)) = 2a^(-6)b^5.`

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