Answer:
![\frac{7^{15}}{3^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B7%5E%7B15%7D%7D%7B3%5E%7B30%7D%7D)
Step-by-step explanation:
The given expression is:
![(\frac{3^{-6}}{7^{-3}})^{5}](https://tex.z-dn.net/?f=%28%5Cfrac%7B3%5E%7B-6%7D%7D%7B7%5E%7B-3%7D%7D%29%5E%7B5%7D)
Moving the expression to the other side in the fraction changes its sign to opposite. A numerator with negative exponent, when written in denominator will have the positive exponent. Using this rule, we can write:
![(\frac{3^{-6}}{7^{-3}})^{5}\\\\ = (\frac{7^{3}}{3^{6}} )^{5}](https://tex.z-dn.net/?f=%28%5Cfrac%7B3%5E%7B-6%7D%7D%7B7%5E%7B-3%7D%7D%29%5E%7B5%7D%5C%5C%5C%5C%20%3D%20%28%5Cfrac%7B7%5E%7B3%7D%7D%7B3%5E%7B6%7D%7D%20%29%5E%7B5%7D)
The exponent 5 can be distributed to both numerator and denominator as shown:
![(\frac{7^{3}}{3^{6}} )^{5}\\\\ = \frac{(7^{3})^{5}}{(3^{6})^{5}}](https://tex.z-dn.net/?f=%28%5Cfrac%7B7%5E%7B3%7D%7D%7B3%5E%7B6%7D%7D%20%29%5E%7B5%7D%5C%5C%5C%5C%20%3D%20%5Cfrac%7B%287%5E%7B3%7D%29%5E%7B5%7D%7D%7B%283%5E%7B6%7D%29%5E%7B5%7D%7D)
The power of a power can be written as a product. i.e.
![\frac{(7^{3})^{5}}{(3^{6})^{5}}\\\\ =\frac{7^{15}}{3^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B%287%5E%7B3%7D%29%5E%7B5%7D%7D%7B%283%5E%7B6%7D%29%5E%7B5%7D%7D%5C%5C%5C%5C%20%3D%5Cfrac%7B7%5E%7B15%7D%7D%7B3%5E%7B30%7D%7D)
So, the expression similar to the given expression and with positive exponents is: ![\frac{7^{15}}{3^{30}}](https://tex.z-dn.net/?f=%5Cfrac%7B7%5E%7B15%7D%7D%7B3%5E%7B30%7D%7D)
Answer:
1 1/2 or 3/2
Step-by-step explanation:
8 1/4 divided by 5 1/2
Convert to improper fraction
33/4 divided by 11/2=66/44
Simplify this to get 1 1/2 or 3/2
Answer:
45000
Step-by-step explanation:
Answer: 1, 2, 4, or 5
Step-by-step explanation:
The relationship in #3 is a function because all the x values are distinct, that is, none are repeated. (Y values don't matter.)
A function will not repeat any x values so if your goal is for the relationship in #4 to NOT be a function, repeat one of the x values. Any one will work.
Answer:
The answer is A: 5x + 10y > 30. That is, the combination of boxes must be greater than 30 since the requirement is to have more than 30 lb of nails.
Step-by-step explanation:
The worker can buy a combination of boxes, as long as the total is greater than 30 lb. Multiply 5 lb by x and add that to 10 lb times y to get the total, which must exceed 30 lb.