Given:
![\text { a. } x^{2}=\frac{4}{9}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20a.%20%7D%20x%5E%7B2%7D%3D%5Cfrac%7B4%7D%7B9%7D)
![\text { b. } x^{3}=\frac{27}{64}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20b.%20%7D%20x%5E%7B3%7D%3D%5Cfrac%7B27%7D%7B64%7D)
![\text { c. } x^{2}=\frac{81}{64}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20c.%20%7D%20x%5E%7B2%7D%3D%5Cfrac%7B81%7D%7B64%7D)
![\text { d. } x^{3}=\frac{1}{8}](https://tex.z-dn.net/?f=%5Ctext%20%7B%20d.%20%7D%20%20x%5E%7B3%7D%3D%5Cfrac%7B1%7D%7B8%7D)
To find:
The value of x for each equation.
Solution:
a) ![x^{2}=\frac{4}{9}](https://tex.z-dn.net/?f=x%5E%7B2%7D%3D%5Cfrac%7B4%7D%7B9%7D)
![x^{2}=\frac{2^2}{3^2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%3D%5Cfrac%7B2%5E2%7D%7B3%5E2%7D)
Taking square root on both sides.
![\sqrt{x^{2}}=\sqrt{ \frac{2^2}{3^2}}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E%7B2%7D%7D%3D%5Csqrt%7B%20%5Cfrac%7B2%5E2%7D%7B3%5E2%7D%7D)
Square and square roots get canceled.
![x =\frac{2}{3}](https://tex.z-dn.net/?f=x%20%3D%5Cfrac%7B2%7D%7B3%7D)
b) ![x^{3}=\frac{27}{64}](https://tex.z-dn.net/?f=x%5E%7B3%7D%3D%5Cfrac%7B27%7D%7B64%7D)
![x^{3}=\frac{3^3}{4^3}](https://tex.z-dn.net/?f=x%5E%7B3%7D%3D%5Cfrac%7B3%5E3%7D%7B4%5E3%7D)
Taking cube root on both sides.
![\sqrt[3]{x^{3}} =\sqrt[3]{\frac{3^3}{4^3} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E%7B3%7D%7D%20%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3%5E3%7D%7B4%5E3%7D%20%7D)
cube and cube roots get canceled.
![x=\frac{3}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%7D%7B4%7D)
c) ![x^{2}=\frac{81}{64}](https://tex.z-dn.net/?f=x%5E%7B2%7D%3D%5Cfrac%7B81%7D%7B64%7D)
![x^{2}=\frac{9^2}{8^2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%3D%5Cfrac%7B9%5E2%7D%7B8%5E2%7D)
Taking square root on both sides.
![\sqrt{x^{2}}=\sqrt{ \frac{9^2}{8^2}}](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E%7B2%7D%7D%3D%5Csqrt%7B%20%5Cfrac%7B9%5E2%7D%7B8%5E2%7D%7D)
Square and square roots get canceled.
![x =\frac{9}{8}](https://tex.z-dn.net/?f=x%20%3D%5Cfrac%7B9%7D%7B8%7D)
d) ![x^{3}=\frac{1}{8}](https://tex.z-dn.net/?f=x%5E%7B3%7D%3D%5Cfrac%7B1%7D%7B8%7D)
![x^{3}=\frac{1^3}{2^3}](https://tex.z-dn.net/?f=x%5E%7B3%7D%3D%5Cfrac%7B1%5E3%7D%7B2%5E3%7D)
Taking cube root on both sides.
![\sqrt[3]{x^{3}} =\sqrt[3]{\frac{1^3}{2^3} }](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%5E%7B3%7D%7D%20%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B1%5E3%7D%7B2%5E3%7D%20%7D)
cube and cube roots get canceled.
![x=\frac{1}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B2%7D)
<h2><u><em>
Answer: 0. 25=88 0.50=44</em></u></h2>
<u><em /></u>
You can buy 8 0.25 cent items because 0.25 · 8 = 2
you can buy 4 0.50 because 4 makes 2 dollars
you then multiply for the 11 students
<h3><em>4 and 11 </em></h3><h3><em>8 and 11</em></h3>
<em />
Answer:
4
Step-by-step explanation:
fourrrrrrr