Question:
Select the three expressions that are equivalent to
:
a: ![(\frac{6^9}{6^8})^2](https://tex.z-dn.net/?f=%28%5Cfrac%7B6%5E9%7D%7B6%5E8%7D%29%5E2)
b: ![\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }](https://tex.z-dn.net/?f=%5Cfrac%7B6%20%2A%206%20%2A%206%20%2A%206%20%2A%206%20%2A%206%20%2A%206%7D%7B6%20%2A%206%20%2A%206%20%7D)
c: ![\frac{6^4}{6^2}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5E4%7D%7B6%5E2%7D)
d: ![\frac{6^5 * 6^7}{6^{10}}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5E5%20%2A%206%5E7%7D%7B6%5E%7B10%7D%7D)
Answer:
a: ![(\frac{6^9}{6^8})^2](https://tex.z-dn.net/?f=%28%5Cfrac%7B6%5E9%7D%7B6%5E8%7D%29%5E2)
c: ![\frac{6^4}{6^2}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5E4%7D%7B6%5E2%7D)
d: ![\frac{6^5 * 6^7}{6^{10}}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5E5%20%2A%206%5E7%7D%7B6%5E%7B10%7D%7D)
Step-by-step explanation:
Given
:
Required
Find equivalent expressions
<em>To solve this question; we'll simplify options a to do, one after the other</em>
a: ![(\frac{6^9}{6^8})^2](https://tex.z-dn.net/?f=%28%5Cfrac%7B6%5E9%7D%7B6%5E8%7D%29%5E2)
From laws of indices;
![\frac{a^m}{a^n} = a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%20%3D%20a%5E%7Bm-n%7D)
This implies that;
![(\frac{6^9}{6^8})^2 = (6^{9-8})^2](https://tex.z-dn.net/?f=%28%5Cfrac%7B6%5E9%7D%7B6%5E8%7D%29%5E2%20%3D%20%286%5E%7B9-8%7D%29%5E2)
![(\frac{6^9}{6^8})^2 = (6^{1})^2](https://tex.z-dn.net/?f=%28%5Cfrac%7B6%5E9%7D%7B6%5E8%7D%29%5E2%20%3D%20%286%5E%7B1%7D%29%5E2)
From laws of indices;
![{a^m}^n = a^{m*n} = a^{mn}](https://tex.z-dn.net/?f=%7Ba%5Em%7D%5En%20%3D%20a%5E%7Bm%2An%7D%20%3D%20a%5E%7Bmn%7D)
This implies that
![(\frac{6^9}{6^8})^2 = (6^{1*2})](https://tex.z-dn.net/?f=%28%5Cfrac%7B6%5E9%7D%7B6%5E8%7D%29%5E2%20%3D%20%286%5E%7B1%2A2%7D%29)
![(\frac{6^9}{6^8})^2 = 6^{2}](https://tex.z-dn.net/?f=%28%5Cfrac%7B6%5E9%7D%7B6%5E8%7D%29%5E2%20%3D%206%5E%7B2%7D)
Hence,
is equivalent to ![6^2](https://tex.z-dn.net/?f=6%5E2)
b. ![\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 }](https://tex.z-dn.net/?f=%5Cfrac%7B6%20%2A%206%20%2A%206%20%2A%206%20%2A%206%20%2A%206%20%2A%206%7D%7B6%20%2A%206%20%2A%206%20%7D)
From laws of indices;
![a^m * a^n = a^{m+n}](https://tex.z-dn.net/?f=a%5Em%20%2A%20a%5En%20%3D%20a%5E%7Bm%2Bn%7D)
This implies that
![\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = \frac{6^{1+1+1+1+1+1}}{6^{1+1+1}}](https://tex.z-dn.net/?f=%5Cfrac%7B6%20%2A%206%20%2A%206%20%2A%206%20%2A%206%20%2A%206%20%2A%206%7D%7B6%20%2A%206%20%2A%206%20%7D%20%20%3D%20%5Cfrac%7B6%5E%7B1%2B1%2B1%2B1%2B1%2B1%7D%7D%7B6%5E%7B1%2B1%2B1%7D%7D)
![\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = \frac{6^{6}}{6^{3}}](https://tex.z-dn.net/?f=%5Cfrac%7B6%20%2A%206%20%2A%206%20%2A%206%20%2A%206%20%2A%206%20%2A%206%7D%7B6%20%2A%206%20%2A%206%20%7D%20%20%3D%20%5Cfrac%7B6%5E%7B6%7D%7D%7B6%5E%7B3%7D%7D)
From laws of indices;
![\frac{a^m}{a^n} = a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%20%3D%20a%5E%7Bm-n%7D)
This implies that
![\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = 6^{6-3}](https://tex.z-dn.net/?f=%5Cfrac%7B6%20%2A%206%20%2A%206%20%2A%206%20%2A%206%20%2A%206%20%2A%206%7D%7B6%20%2A%206%20%2A%206%20%7D%20%20%3D%206%5E%7B6-3%7D)
![\frac{6 * 6 * 6 * 6 * 6 * 6 * 6}{6 * 6 * 6 } = 6^{3}](https://tex.z-dn.net/?f=%5Cfrac%7B6%20%2A%206%20%2A%206%20%2A%206%20%2A%206%20%2A%206%20%2A%206%7D%7B6%20%2A%206%20%2A%206%20%7D%20%20%3D%206%5E%7B3%7D)
Hence;
is not equivalent to ![6^2](https://tex.z-dn.net/?f=6%5E2)
c. ![\frac{6^4}{6^2}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5E4%7D%7B6%5E2%7D)
From laws of indices;
![\frac{a^m}{a^n} = a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%20%3D%20a%5E%7Bm-n%7D)
This implies that
![\frac{6^4}{6^2} = 6^{4-2}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5E4%7D%7B6%5E2%7D%20%3D%206%5E%7B4-2%7D)
![\frac{6^4}{6^2} = 6^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5E4%7D%7B6%5E2%7D%20%3D%206%5E%7B2%7D)
Hence,
is equivalent to ![6^2](https://tex.z-dn.net/?f=6%5E2)
d. ![\frac{6^5 * 6^7}{6^{10}}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5E5%20%2A%206%5E7%7D%7B6%5E%7B10%7D%7D)
From laws of indices;
![a^m * a^n = a^{m+n}](https://tex.z-dn.net/?f=a%5Em%20%2A%20a%5En%20%3D%20a%5E%7Bm%2Bn%7D)
This implies that
![\frac{6^5 * 6^7}{6^{10}} = \frac{6^{5+7}}{6^{10}}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5E5%20%2A%206%5E7%7D%7B6%5E%7B10%7D%7D%20%3D%20%5Cfrac%7B6%5E%7B5%2B7%7D%7D%7B6%5E%7B10%7D%7D)
From laws of indices;
![\frac{a^m}{a^n} = a^{m-n}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5Em%7D%7Ba%5En%7D%20%3D%20a%5E%7Bm-n%7D)
This implies that
![\frac{6^5 * 6^7}{6^{10}} = 6^{5+7-10}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5E5%20%2A%206%5E7%7D%7B6%5E%7B10%7D%7D%20%3D%206%5E%7B5%2B7-10%7D)
![\frac{6^5 * 6^7}{6^{10}} = 6^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B6%5E5%20%2A%206%5E7%7D%7B6%5E%7B10%7D%7D%20%3D%206%5E%7B2%7D)
Hence,
is equivalent to ![6^2](https://tex.z-dn.net/?f=6%5E2)
1.85 meters=6.06955381 feet
1.85 meters=72.8346457 inches
18321.8
Step by step explanation This is how I got the answer to your question and I gave you the solution I hope this helps you out
Answer:
x = 2 or 1/4
Step-by-step explanation:
by solving it we get ;
=》
![4 {x}^{2} - 9x + 2 = 0](https://tex.z-dn.net/?f=4%20%7Bx%7D%5E%7B2%7D%20%20-%209x%20%2B%202%20%3D%200)
=》
![4 {x}^{2} - 8x - x + 2](https://tex.z-dn.net/?f=4%20%7Bx%7D%5E%7B2%7D%20%20-%208x%20-%20x%20%2B%202)
=》
![4x(x - 2) - 1(x - 2)](https://tex.z-dn.net/?f=4x%28x%20-%202%29%20%20-%201%28x%20-%202%29)
=》
![(4x - 1)(x - 2)](https://tex.z-dn.net/?f=%284x%20-%201%29%28x%20-%202%29)
so,
![x = 2 \: \: or \: \: \frac{1}{4}](https://tex.z-dn.net/?f=x%20%3D%202%20%5C%3A%20%5C%3A%20%20or%20%20%5C%3A%20%20%5C%3A%20%5Cfrac%7B1%7D%7B4%7D%20)
<em>i</em><em> </em><em>hope</em><em> </em><em>it</em><em> </em><em>helped</em><em>.</em><em>.</em><em>.</em><em>.</em><em>.</em>