It's a perfect square because 8 times 8 equals 64.
It is ten units, as the two sides are of 6 and 8 so you must square them both, add them together (which gives you 100) and then square root that, which gives you 10
Find the number that when multiplied with 350 will give you 24.5. This number happens to be .07 or in terms of sales tax, 7%.
Answer:
18
Step-by-step explanation:
w varies directly with z, let k be the constant of proportionality, hence this can be represented by the equation:
w = kz
When z = 4, w = 12, hence we need to find the value of the constant of proportionality, substituting:
12 = 4k
Dividing both sides by 4:
12/4 = 4k/4
k = 3
Therefore the equation becomes:
w = 3z
The value of w when z = 6 is given as:
w = 3(6)
w = 18
The main rule we use in this exercise is

and the more general case:
![( \sqrt[n]{a} ) ^{m} =( a^{ \frac{1}{n}} )^{m} = a^{ \frac{1}{n}*m}=a^{ \frac{m}{n}}](https://tex.z-dn.net/?f=%28%20%20%5Csqrt%5Bn%5D%7Ba%7D%20%20%29%20%5E%7Bm%7D%20%3D%28%20a%5E%7B%20%5Cfrac%7B1%7D%7Bn%7D%7D%20%29%5E%7Bm%7D%20%3D%20a%5E%7B%20%5Cfrac%7B1%7D%7Bn%7D%2Am%7D%3Da%5E%7B%20%5Cfrac%7Bm%7D%7Bn%7D%7D)
Using these rules, we make all the indices, or exponents, look like

, and compare them to each other.
A.

B.

C.
![( \sqrt[3]{125} ) ^{7} =( 125^{ \frac{1}{3}} )^{7} = 125^{ \frac{1}{3}*7}= 125^{ \frac{7}{3}}](https://tex.z-dn.net/?f=%28%20%20%5Csqrt%5B3%5D%7B125%7D%20%29%20%5E%7B7%7D%20%3D%28%20125%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%7D%20%29%5E%7B7%7D%20%3D%20125%5E%7B%20%20%5Cfrac%7B1%7D%7B3%7D%2A7%7D%3D%20125%5E%7B%20%5Cfrac%7B7%7D%7B3%7D%7D%20%20%20)
D.