Question

1. Simplify the Expression √36x^2/y^7

2. Simplify the Expression (1-3i)(2+5i)-(3-12i)


3. The formula c= √a^2+b^2 represents the length of the hypotenuse of a right triangle with side lengths a and b. Solve the equation for a. Show your work. That means get "a" all by itself on one side of the equation.

Answer 1

See below

Explanation:

1.

`\sqrt{(36x^(2))/(y^(7))} \\= \sqrt{(6^(2)x^(2))/(y^(6)y)} \\=(6x)/(y^(3)√(y) ) \\=(6x√(y))/(y^(4) ) \\`

2.

`(1-3i)(2+5i)-(3-12i)\\=2+5i-6i-15i^(2)-3+12i\\=14+11i`

** i^2=-1, -15i^2 = 15

3.

`c=\sqrt{a^(2)+b^(2)} \\c^(2)=a^(2)+b^(2)\\a^(2)=c^(2)-b^(2)\\a=\sqrt{c^(2)-b^(2)}`