Q1. The answer is <span>1 over 5 to the 3rd power.
</span>5 to the 5th is 5⁵
5 to the 8th is 5⁸
5 to the 5th over 5 to the 8th is
![\frac{ 5^{5} }{ 5^{8} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%205%5E%7B5%7D%20%7D%7B%205%5E%7B8%7D%20%7D%20)
To simplify, we will use two rules:
![\frac{ x^{a}}{ x^{b} } = x^{a-b} \\ x^{-a} = \frac{1}{ x^{a}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20x%5E%7Ba%7D%7D%7B%20x%5E%7Bb%7D%20%7D%20%3D%20x%5E%7Ba-b%7D%20%5C%5C%20x%5E%7B-a%7D%20%3D%20%5Cfrac%7B1%7D%7B%20x%5E%7Ba%7D%7D%20)
Therefore:
![\frac{ 5^{5} }{ 5^{8} } = 5^{5-8} =5^{-3}= \frac{1}{5^{3}}](https://tex.z-dn.net/?f=%5Cfrac%7B%205%5E%7B5%7D%20%7D%7B%205%5E%7B8%7D%20%7D%20%3D%205%5E%7B5-8%7D%20%3D5%5E%7B-3%7D%3D%20%5Cfrac%7B1%7D%7B5%5E%7B3%7D%7D%20)
![\frac{1}{5^{3}}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B5%5E%7B3%7D%7D%20)
is the same as 1 over 5 to the 3rd power.
Q2. The answer is <span>(53)−4.
The exponents are multiplied when are expressed in the form:
</span>
![(x^{a}) ^{b}= x^{a*b}](https://tex.z-dn.net/?f=%20%28x%5E%7Ba%7D%29%20%5E%7Bb%7D%3D%20x%5E%7Ba%2Ab%7D)
So,
![(5^{3} )^{-4}=5^{3*(-4)}=5^{-12}](https://tex.z-dn.net/?f=%20%285%5E%7B3%7D%20%29%5E%7B-4%7D%3D5%5E%7B3%2A%28-4%29%7D%3D5%5E%7B-12%7D)
Other choices are incorrect:
<span>one third to the 4th times one third to the 7th is </span>
![( \frac{1}{3} )^{4} *( \frac{1}{3} )^{7}=( \frac{1}{3} )^{4+7}](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B1%7D%7B3%7D%20%29%5E%7B4%7D%20%2A%28%20%5Cfrac%7B1%7D%7B3%7D%20%29%5E%7B7%7D%3D%28%20%5Cfrac%7B1%7D%7B3%7D%20%29%5E%7B4%2B7%7D)
3 to the 7th over 3 to the 15th is
![\frac{ 3^{7} }{3^{15}} =3^{7-15}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%203%5E%7B7%7D%20%7D%7B3%5E%7B15%7D%7D%20%3D3%5E%7B7-15%7D)
<span>45 ⋅ 42 is </span>
-2Y^2+24Y+X. Is the simplified version of this. <span />
Answer:
that is confusinnnnnnnnnggggggggggg!!!! try to look on google to see if it helps! thats what i do sometimes!!!!
Answer:
3 gulps
Step-by-step explanation:
In this problem, f(x) = 3. Plug this into the equation:
3 = -3x + 12
Solve for x:
3 - 12 = -3x + 12 - 12
-9 = -3x
-9 / -3 = -3x / -3
3 = x
3 gulps
Answer:
A ≈ 81.487 in²
Step-by-step explanation:
You know that circumference is C = 2πr, where r is the radius.
So,
C = 2πr
32 = 2(3.14)r
r ≈ 5.093 in
We also know that the formula for the area of a circle is A = πr², so:
A = πr²
A = (3.14)(5.093)²
A ≈ 81.487 in²