The solution to the given indices are 1/2^7, 11^4 and -1/64
<h3>Indices expression</h3>
Give the following indices expression
![\frac{(2^{-4})^2\times 2^{-5}}{2^{-6}} \\](https://tex.z-dn.net/?f=%5Cfrac%7B%282%5E%7B-4%7D%29%5E2%5Ctimes%202%5E%7B-5%7D%7D%7B2%5E%7B-6%7D%7D%20%5C%5C)
This can be further simplified according to the law of indices as:
![\frac{(2^{-4})^2\times 2^{-5}}{2^{-6}} =\frac{2^{-8-5}}{2^{-6}}](https://tex.z-dn.net/?f=%5Cfrac%7B%282%5E%7B-4%7D%29%5E2%5Ctimes%202%5E%7B-5%7D%7D%7B2%5E%7B-6%7D%7D%20%3D%5Cfrac%7B2%5E%7B-8-5%7D%7D%7B2%5E%7B-6%7D%7D)
Determine the result
![\frac{2^{-8-5}}{2^{-6}} = 2^{-7} = 1/2^7](https://tex.z-dn.net/?f=%5Cfrac%7B2%5E%7B-8-5%7D%7D%7B2%5E%7B-6%7D%7D%20%3D%202%5E%7B-7%7D%20%3D%201%2F2%5E7)
For the indices expression
![11^{-4}\times 11^{8} = 11^{-4+8}=11^4](https://tex.z-dn.net/?f=11%5E%7B-4%7D%5Ctimes%2011%5E%7B8%7D%20%3D%2011%5E%7B-4%2B8%7D%3D11%5E4)
For the indices expression
![-4^4\times4^{-7}\\=-(4^{4-7})\\= -4^{-3}\\=-1/4^3\\=-1/64](https://tex.z-dn.net/?f=-4%5E4%5Ctimes4%5E%7B-7%7D%5C%5C%3D-%284%5E%7B4-7%7D%29%5C%5C%3D%20-4%5E%7B-3%7D%5C%5C%3D-1%2F4%5E3%5C%5C%3D-1%2F64)
Hence the solution to the given indices are 1/2^7, 11^4 and -1/64
Learn more on indices here: brainly.com/question/170984
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3^5) (x + 2)^(3/2) + 3 = 27
<span>(x + 2)^(3/2) = 24 / 243 </span>
<span>x + 2 = [ 24 / 243 ]^(2/3) </span>
<span>x + 2 = [ 8 / 81 ]^(2/3) </span>
<span>x = [ 4 / 81^(2/3) ] - 2 =-1.786
the answer is x=-1.786</span>
B) is the answer because of alternate angles meaning that <DEB IS equal to <EBC AND if you take away 180 from the angles (angles on a straight line are 180) then they will both give you the same answer