MTH 121
Exam 1, Form B
Spring 2013
No calculators.
These formulas may or may not be useful:
a3+b3=(a+b)(a2−ab+b2) a3−b3=(a−b)(a2+ab+b2)
(For this exam, assume any variables represent positive numbers.)
Justify your answers with neat and organized work.
100 points possible.
1. Use absolute value notation to describe the situation.
The distance between x and 4 is no more than 7.
2. Evaluate the expression for the given value of x.
x2−4x−3 x=−3
3. Perform the operation and simplify:
2
3
−
5
6
+
3
4
4. Perform the operation and simplify:
30÷
1
5
5. Put in simplest exponential form: (1) no radicals, and (2) positive
exponents only.
⎛ ⎝
23x−2y3
2x6y−1
⎞ ⎠
−3
6. Put in simplest exponential form: (1) no radicals, and (2) positive
exponents only.
(6a−2c5)2
(2a4c)3
7. The radicand is a perfect power. Find the specified root.
√
c4t16
8. The radicand is a perfect power. Find the specified root.
3 ⎛ √
64
125
w27
9. Simplify by removing perfect powers from the radicand.
Leave the radical sign in your answer.
3
√
−x10w7
10. Simplify by removing perfect powers from the radicand.
Leave the radical sign in your answer.
4 ⎛ √
81c5t16
16x10a7
11. Put in simplest exponential form: (1) no radicals, and (2) positive
exponents only.
w1/4 w8
12. Put in simplest exponential form: (1) no radicals, and (2) positive
exponents only.
⎛ ⎝
16a6
25w16
⎞ ⎠
3/2
13. Put in simplest exponential form: (1) no radicals, and (2) positive
exponents only.
( x3/4 b4 )4
14. Put in simplest exponential form: (1) no radicals, and (2) positive
exponents only.