Answer:
The seventh root of a^5
Step-by-step explanation:

is equal to
![\sqrt[7]{a^5}](https://tex.z-dn.net/?f=%5Csqrt%5B7%5D%7Ba%5E5%7D)
because
![b^{1/m} = \sqrt[m]{b}](https://tex.z-dn.net/?f=b%5E%7B1%2Fm%7D%20%3D%20%5Csqrt%5Bm%5D%7Bb%7D)
hope this makes sense and helps
we have that

I. Rewrite the equation by substituting the expression u in for sin x.

II. Factor the quadratic expression. Rewrite the equation with factors instead of the original polynomial.
is equal to
using a graph calculator-----> see the attached figure

III. Use the zero product property to solve the quadratic equation.

(u-3)=0--------------> u=3
(2u+1)=0-------- 2u=-1------> u=-1/2-----> u=-0.5
IV. Rewrite your solutions to Part III by replacing u with sin x.
sin x=3--------> is not the solution (sin x can not be greater than 1)
sin x=-0.50------>is the solution
V. Solve the remaining equations for x, giving all solutions to the equation.
sin x=-0.50
if the sine is negative
then
x belong to the III or IV quadrant
we know that
sin 30°=0.50
so
the solution for the III quadrant is
x=180°+30°-------> x=210°
the solution for the IV quadrant is
x=360°-30°------> x=330°
Since they each paid the same amount, we can figure out that 9*4=36 dollars is the price of the gift. Next, since there was a 10% discount (or 0.1 by moving the decimal 2 spots to the left), we can say that the original gift price is x and
x-0.1*x=0.9*x due to that we subtract the 10% discount (and it's 10% of the original price). In addition, the sisters paid 0.9*x, which is 36. Dividing both sides by 0.9, we get x=40