Download Chapter 10

Name
Chapter 10 Test
Math 152 – Bloom
√
1. Rewrite 8 3 x2 y as an exponential expression.
5
3
2. Rewrite 2m /2 n /2 as a radical expression.
3. Simplify i14
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4. Simplify −96
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5. Let f (x) = 14 − 3x
(a) Find the exact value of f (− 32 )
(b) Find the exact value of f (2)
6. Explain how to find the value of 81−3/4 without using a calculator.
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7. Rationalize the denominator of the expression √
2 3−4
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8. Simplify 18x3 y 6 .
9. Simplify the following using the rules of exponents. Assume all variables represent positive
numbers.
√ 3
x /4 y 5
(a) √ 1
x /4 y 7
√
3
(b) x4 · x3/4
(c) (27a2/3 b12 )1/3
10. Completely simplify the following radical expressions. All answers should be exact.
√
√
√
(a) 5 5 + 6 20 − 4 18
√
√
√
(b) ( 6 − 3)( 2 − 3)
11. Completely simplify the following expressions. Be sure to write your answers in the proper
form.
(a) (6 − 5i)(4 + 2i)
2 + 4i
(b)
3 − 5i
12. Solve the following equations.
√
(a) 2x − 4 − 5 = 1
√
√
(b) 2x − 1 + x = 2
13. Consider a triangle whose vertices are located at the points (1, 3), (7, 3), and (7, 6), as shown:
(7, 6)
3 units
b
(1, 3)
b
b
6 units
(7, 3)
• What is the midpoint of the hypotenuse of the triangle?
• Use the distance formula to calculate the length of the hypotenuse.
• Use the Pythagorean Theorem to confirm that this is a right triangle.