Download Math 125 Sample Test 3 1. Simplify. Use positive exponents. (a) (a

Math 125 Sample Test 3
1. Simplify. Use positive exponents.
1
(a) a 6
3
a4
1
(b)
a 3 b−4
1
a 2 b−3
√
−12
3
(c)
a−4 b3
2
(d) 8− 3
(e) a−9 b6
− 2
3
2. Simplify. Assume that each variable can represent any real number.
√
(a) 16x2 y 4
√
(b) x2 + 6x + 9
√
(c) 3 8y 3 z 6
√
(d) 4 16x4 y 16
3. Simplify. Assume variables represent nonnegative numbers.
√
3
(a) −8a4 b11 c
√
√
4
4
(b) 4x5 12x2
√
√
√
(c) 4 − 75 + 5 − 2
√
√
√
√
(d) 8 − 6 + 2 + 12
4. Multiply.
√
(a) ( 2 + x)2
√
√
√ √
(b) ( 2 − 2 3)( 2 + 2 3)
5. Write the expression using a single radical notation in simplest form.
q√
4
3
4x2
√
√
6
8
(b) 2 3
(a)
6. Simplify. Write complex expressions in a + bi form.
(a) (−3 + 4i)(5 − 2i)
2 − 3i
(b)
1 + 2i
(c) i142
(d) i−21
7. Rationalize denominator.
1
2xy
8x2 yz 4
√
1+ 2
√
(b)
3− 2
(a) √
5
8. Solve.
3
(a) (2 − 3x)− 2 = 27
√
√
(b) 2x − 1 − 4x + 5 = −2
9. Solve the equation by completing the square.
2x2 − 6x + 3 = 0
10. (a) Find the distance between (−2, −4) and (3, −1).
(b) Find the midpoint of (−2, −4) and (3, −1).
2