Answer:
Yyyxyw
Step-by-step explanation:
Ez
Answer:
+15 degrees
Step-by-step explanation:
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
ANSWER
![\frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 25a ^{9} b^{10} }{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B%285ab%29%7D%5E%7B3%7D%20%7D%7B30%20%7Ba%7D%5E%7B%20-%206%7D%20%20%7Bb%7D%5E%7B%20-%207%7D%20%7D%20%20%3D%20%20%5Cfrac%7B%2025a%20%5E%7B9%7D%20b%5E%7B10%7D%20%7D%7B6%7D%20)
EXPLANATION
To find the expression that is equivalent to
![\frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B%285ab%29%7D%5E%7B3%7D%20%7D%7B30%20%7Ba%7D%5E%7B%20-%206%7D%20%20%7Bb%7D%5E%7B%20-%207%7D%20%7D%20)
we must simplify it.
We apply the laws of exponents in the simplification.
First, let us share the cubic exponent for each factor in the numerator to obtain,
![\frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 5^{3}a ^{3} b^{3} }{30 {a}^{ - 6} {b}^{ - 7} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B%285ab%29%7D%5E%7B3%7D%20%7D%7B30%20%7Ba%7D%5E%7B%20-%206%7D%20%20%7Bb%7D%5E%7B%20-%207%7D%20%7D%20%20%3D%20%20%5Cfrac%7B%205%5E%7B3%7Da%20%5E%7B3%7D%20b%5E%7B3%7D%20%7D%7B30%20%7Ba%7D%5E%7B%20-%206%7D%20%20%7Bb%7D%5E%7B%20-%207%7D%20%7D%20)
This gives us,
![\frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 125a ^{3} b^{3} }{30 {a}^{ - 6} {b}^{ - 7} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B%285ab%29%7D%5E%7B3%7D%20%7D%7B30%20%7Ba%7D%5E%7B%20-%206%7D%20%20%7Bb%7D%5E%7B%20-%207%7D%20%7D%20%20%3D%20%20%5Cfrac%7B%20125a%20%5E%7B3%7D%20b%5E%7B3%7D%20%7D%7B30%20%7Ba%7D%5E%7B%20-%206%7D%20%20%7Bb%7D%5E%7B%20-%207%7D%20%7D%20)
We simplify by applying the following law of exponent,
![\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7Ba%7D%5E%7Bm%7D%20%7D%7B%20%7Ba%7D%5E%7Bn%7D%20%7D%20%20%3D%20%20%7Ba%7D%5E%7Bm%20-%20n%7D%20)
Our expression now becomes,
![\frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 25a ^{3 - - 6} b^{3 - - 7} }{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B%285ab%29%7D%5E%7B3%7D%20%7D%7B30%20%7Ba%7D%5E%7B%20-%206%7D%20%20%7Bb%7D%5E%7B%20-%207%7D%20%7D%20%20%3D%20%20%5Cfrac%7B%2025a%20%5E%7B3%20-%20%20-%206%7D%20b%5E%7B3%20-%20%20-%207%7D%20%7D%7B6%7D%20)
We simplify further to get,
![\frac{ {(5ab)}^{3} }{30 {a}^{ - 6} {b}^{ - 7} } = \frac{ 25a ^{3 + 6} b^{3 + 7} }{6}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B%285ab%29%7D%5E%7B3%7D%20%7D%7B30%20%7Ba%7D%5E%7B%20-%206%7D%20%20%7Bb%7D%5E%7B%20-%207%7D%20%7D%20%20%3D%20%20%5Cfrac%7B%2025a%20%5E%7B3%20%20%2B%20%206%7D%20b%5E%7B3%20%20%2B%207%7D%20%7D%7B6%7D%20)
This finally gives us,
Answer:
![a_n = -5 +(n-1)*2](https://tex.z-dn.net/?f=a_n%20%3D%20-5%20%2B%28n-1%29%2A2)
Step-by-step explanation:
<u>Step 1: Determine the variables</u>
Initial number is -5
Increments of +2
<u>Step 2: Create an explicit formula</u>
![a_n = initial+(n-1)*increment](https://tex.z-dn.net/?f=a_n%20%3D%20initial%2B%28n-1%29%2Aincrement)
![a_n = -5 +(n-1)*2](https://tex.z-dn.net/?f=a_n%20%3D%20-5%20%2B%28n-1%29%2A2)
Answer: ![a_n = -5 +(n-1)*2](https://tex.z-dn.net/?f=a_n%20%3D%20-5%20%2B%28n-1%29%2A2)