Answer:
![8^{\left(-8\times \:8\right)^6}=8^{64^6}](https://tex.z-dn.net/?f=8%5E%7B%5Cleft%28-8%5Ctimes%20%5C%3A8%5Cright%29%5E6%7D%3D8%5E%7B64%5E6%7D)
Step-by-step explanation:
Given the expression
![8^{\left(-8\times \:8\right)^6}](https://tex.z-dn.net/?f=8%5E%7B%5Cleft%28-8%5Ctimes%20%5C%3A8%5Cright%29%5E6%7D)
Let the expression
![8^{\left(-8\times \:8\right)^6}.....[A]](https://tex.z-dn.net/?f=8%5E%7B%5Cleft%28-8%5Ctimes%20%5C%3A8%5Cright%29%5E6%7D.....%5BA%5D)
first solving
![\left(-8\times \:8\right)^6](https://tex.z-dn.net/?f=%5Cleft%28-8%5Ctimes%20%5C%3A8%5Cright%29%5E6)
![\mathrm{Multiply\:the\:numbers:}\:8\times \:8=64](https://tex.z-dn.net/?f=%5Cmathrm%7BMultiply%5C%3Athe%5C%3Anumbers%3A%7D%5C%3A8%5Ctimes%20%5C%3A8%3D64)
![=\left(-64\right)^6](https://tex.z-dn.net/?f=%3D%5Cleft%28-64%5Cright%29%5E6)
![\mathrm{Apply\:exponent\:rule}:\quad \left(-a\right)^n=a^n,\:\mathrm{if\:}n\mathrm{\:is\:even}](https://tex.z-dn.net/?f=%5Cmathrm%7BApply%5C%3Aexponent%5C%3Arule%7D%3A%5Cquad%20%5Cleft%28-a%5Cright%29%5En%3Da%5En%2C%5C%3A%5Cmathrm%7Bif%5C%3A%7Dn%5Cmathrm%7B%5C%3Ais%5C%3Aeven%7D)
![\left(-64\right)^6=64^6](https://tex.z-dn.net/?f=%5Cleft%28-64%5Cright%29%5E6%3D64%5E6)
![=64^6](https://tex.z-dn.net/?f=%3D64%5E6)
so expression [A] becomes
![=8^{64^6}](https://tex.z-dn.net/?f=%3D8%5E%7B64%5E6%7D)
Therefore,
<h3>Conner work is correct. Jana work is wrong</h3>
<em><u>Solution:</u></em>
<em><u>Given that,</u></em>
<em><u>Conner and Jana are multiplying:</u></em>
![(3^56^8)(3^96^{10})](https://tex.z-dn.net/?f=%283%5E56%5E8%29%283%5E96%5E%7B10%7D%29)
Given Conner's work is:
![(3^56^8)(3^96^{10}) = 3^{5+9}6^{8+10} = 3^{14}6^{18}](https://tex.z-dn.net/?f=%283%5E56%5E8%29%283%5E96%5E%7B10%7D%29%20%3D%203%5E%7B5%2B9%7D6%5E%7B8%2B10%7D%20%3D%203%5E%7B14%7D6%5E%7B18%7D)
We have to check if this work is correct
Yes, Conner work is correct
From given,
![(3^56^8)(3^96^{10})\\\\3^5 \times 6^8 \times 3^9 \times 6^{10}](https://tex.z-dn.net/?f=%283%5E56%5E8%29%283%5E96%5E%7B10%7D%29%5C%5C%5C%5C3%5E5%20%5Ctimes%206%5E8%20%5Ctimes%203%5E9%20%5Ctimes%206%5E%7B10%7D)
Use the following law of exponent
![a^m \times a^n = a^{m+n}](https://tex.z-dn.net/?f=a%5Em%20%5Ctimes%20a%5En%20%3D%20a%5E%7Bm%2Bn%7D)
Therefore,
![3^5 \times 6^8 \times 3^9 \times 6^{10} = 3^5 \times 3^9 \times 6^8 \times 6^{10} = 3^{5+9} \times 6^{8+10} = 3^{14} \times 6^{18}](https://tex.z-dn.net/?f=3%5E5%20%5Ctimes%206%5E8%20%5Ctimes%203%5E9%20%5Ctimes%206%5E%7B10%7D%20%3D%203%5E5%20%5Ctimes%203%5E9%20%5Ctimes%206%5E8%20%5Ctimes%206%5E%7B10%7D%20%3D%203%5E%7B5%2B9%7D%20%5Ctimes%206%5E%7B8%2B10%7D%20%3D%203%5E%7B14%7D%20%5Ctimes%206%5E%7B18%7D)
<em><u>Given Jana's work is:</u></em>
![(3^56^8)(3^96^{10}) = 3^{5.9}6^{8.10} = 3^{45}6^{80}](https://tex.z-dn.net/?f=%283%5E56%5E8%29%283%5E96%5E%7B10%7D%29%20%3D%203%5E%7B5.9%7D6%5E%7B8.10%7D%20%3D%203%5E%7B45%7D6%5E%7B80%7D)
This is incorrect
The powers of same base has to be added. But here, powers are multiplied which is wrong
Let's solve your equation step-by-step.
<span><span><span>4s</span>−<span>4<span>s2</span></span></span>=1
</span>Step 1: Simplify both sides of the equation.
<span><span><span>−<span>4<span>s2</span></span></span>+<span>4s</span></span>=1
</span>Step 2: Subtract 1 from both sides.
<span><span><span><span>−<span>4<span>s2</span></span></span>+<span>4s</span></span>−1</span>=<span>1−1
</span></span><span><span><span><span>−<span>4<span>s2</span></span></span>+<span>4s</span></span>−1</span>=0
</span>Step 3: Factor left side of equation.
<span><span><span>(<span><span>−<span>2s</span></span>+1</span>)</span><span>(<span><span>2s</span>−1</span>)</span></span>=0
</span>Step 4: Set factors equal to 0.
<span><span><span><span>−<span>2s</span></span>+1</span>=<span><span><span>0<span> or </span></span><span>2s</span></span>−1</span></span>=<span>0
s = 1/2</span></span>