<h3>
Answer: Choice A which is (m+6)^2</h3>
Explanation:
Think of two numbers that multiply to 36 and add to 12. Those two numbers are 6 and 6
6+6 = 12
6*6 = 36
So we can factor it into (m+6)(m+6). Use the FOIL rule to expand it out to get m^2+12m+36 back again.
The expression (m+6)(m+6) is the same as (m+6)^2
Answer:
3/5 or 0.6
Step-by-step explanation:
−
5
c
+
16.5
=
13.5
−
5
c
=
−
3
c=3/5
c=0.6
Option C: ![(6^{-4})^{-4}](https://tex.z-dn.net/?f=%286%5E%7B-4%7D%29%5E%7B-4%7D)
Option D: ![(6^{-2})^{-8}](https://tex.z-dn.net/?f=%286%5E%7B-2%7D%29%5E%7B-8%7D)
Option F: ![(6^8)^2](https://tex.z-dn.net/?f=%286%5E8%29%5E2)
Solution:
Given expression: ![6^{16}](https://tex.z-dn.net/?f=6%5E%7B16%7D)
To find which expression is equivalent to the given expression.
Let us solve this using exponent rule: ![\left(a^{b}\right)^{c}=a^{b c}](https://tex.z-dn.net/?f=%5Cleft%28a%5E%7Bb%7D%5Cright%29%5E%7Bc%7D%3Da%5E%7Bb%20c%7D)
Option A: ![(6^{0})^{16}](https://tex.z-dn.net/?f=%286%5E%7B0%7D%29%5E%7B16%7D)
![(6^{0})^{16}=6^{0 \times 16}= 6^0](https://tex.z-dn.net/?f=%286%5E%7B0%7D%29%5E%7B16%7D%3D6%5E%7B0%20%5Ctimes%2016%7D%3D%206%5E0)
It is not equivalent expression.
Option B: ![(6^8)^8](https://tex.z-dn.net/?f=%286%5E8%29%5E8)
![(6^{8})^{8}=6^{8 \times 8}= 6^{64}](https://tex.z-dn.net/?f=%286%5E%7B8%7D%29%5E%7B8%7D%3D6%5E%7B8%20%5Ctimes%208%7D%3D%206%5E%7B64%7D)
It is not equivalent expression.
Option C: ![(6^{-4})^{-4}](https://tex.z-dn.net/?f=%286%5E%7B-4%7D%29%5E%7B-4%7D)
![(6^{-4})^{-4}=6^{(-4 )\times (-4)}= 6^{16}](https://tex.z-dn.net/?f=%286%5E%7B-4%7D%29%5E%7B-4%7D%3D6%5E%7B%28-4%20%29%5Ctimes%20%28-4%29%7D%3D%206%5E%7B16%7D)
It is equivalent expression for the given expression.
Option D: ![(6^{-2})^{-8}](https://tex.z-dn.net/?f=%286%5E%7B-2%7D%29%5E%7B-8%7D)
![(6^{-2})^{-8}=6^{(-2) \times (-8)}= 6^{16}](https://tex.z-dn.net/?f=%286%5E%7B-2%7D%29%5E%7B-8%7D%3D6%5E%7B%28-2%29%20%5Ctimes%20%28-8%29%7D%3D%206%5E%7B16%7D)
It is equivalent expression for the given expression.
Option E: ![(6^{-1})^{16}](https://tex.z-dn.net/?f=%286%5E%7B-1%7D%29%5E%7B16%7D)
![(6^{-1})^{16}=6^{(-1) \times 16}= 6^{-16}](https://tex.z-dn.net/?f=%286%5E%7B-1%7D%29%5E%7B16%7D%3D6%5E%7B%28-1%29%20%5Ctimes%2016%7D%3D%206%5E%7B-16%7D)
It is not equivalent expression.
Option F: ![(6^8)^2](https://tex.z-dn.net/?f=%286%5E8%29%5E2)
![(6^{8})^{2}=6^{8 \times 2}= 6^{16}](https://tex.z-dn.net/?f=%286%5E%7B8%7D%29%5E%7B2%7D%3D6%5E%7B8%20%5Ctimes%202%7D%3D%206%5E%7B16%7D)
It is equivalent expression for the given expression.
Hence
are the equivalent expressions.
Option C, Option D and Option F are correct answers.
Is the missing side a leg or the hypotenuse?