Answer: 49+64i
Step-by-step explanation:
Concept to know:
i=√-1
i²=-1
i³=-i
=1
-------------------------------------
(-5+8i)(3-8i)
=-15+40i+24i-64i²
=-15+64i-64i²
=-15+64i+64 (remember, i²=-1)
=49+64i
Hope this helps!! :)
Please let me know if you have any question or need further explanation
Answer:

Step-by-step explanation:
The expression to transform is:
![(\sqrt[6]{x^5})^7](https://tex.z-dn.net/?f=%28%5Csqrt%5B6%5D%7Bx%5E5%7D%29%5E7)
Let's work first on the inside of the parenthesis.
Recall that the n-root of an expression can be written as a fractional exponent of the expression as follows:
![\sqrt[n]{a} = a^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%7D%20%3D%20a%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
Therefore ![\sqrt[6]{a} = a^{\frac{1}{6}}](https://tex.z-dn.net/?f=%5Csqrt%5B6%5D%7Ba%7D%20%3D%20a%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D)
Now let's replace
with
which is the algebraic form we are given inside the 6th root:
![\sqrt[6]{x^5} = (x^5)^{\frac{1}{6}}](https://tex.z-dn.net/?f=%5Csqrt%5B6%5D%7Bx%5E5%7D%20%3D%20%28x%5E5%29%5E%7B%5Cfrac%7B1%7D%7B6%7D%7D)
Now use the property that tells us how to proceed when we have "exponent of an exponent":

Therefore we get: 
Finally remember that this expression was raised to the power 7, therefore:
[/tex]
An use again the property for the exponent of a exponent:
Answer:
40 pencil cases
Step-by-step explanation:
To find out how many $2.50 pencil cases you can buy with $100, you need to divide. Dividing the amount of money you have by the cost of the item will get you the amount of items you can buy. 100 divided by 2.50 is 40. So, you can get 40 cases.
66 (Joseph's books) +31 (Gilda's books) +31 (Mark's books)= 128 Number of books all together.
There really doesn't need to be a separate explanation for each number because 1 explanation would explain everyone of them.
All of these numbers are rational because a rational number is, or can be, turned into a fraction.
-2 = -2/1
3 = 3/1
819 = 819/1
1,476 = 1,476/1
-6.01 = -6 1/100 = -601/100