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Review
Math 1010
Exam 4
Simplify using only positive exponents. Leave the answer in exponential notation.
2
7
 3x 2 y 5 
 6 2 
 x y 
36a 2b5
4a 6b9
3
(4 x y )(5 xy )
2
Simplify. Assume that variables can represent any value.
81x 2
For the given function, find the indicated function value, if it exists. If the value does not exist, answer “Does
not exist”.
For f ( x) 
3
x  5 find f  22 
For f ( x) 
4
x  5 find f  20 
Determine the domain of the function. Express your answer in interval notation.
f ( x)  4 x  5
Write an equivalent expression using radical notation and, if possible, simplify. Assume that even roots are of
nonnegative quantities.
1
6 7
x y 
5
Use the laws of exponents to simplify. Do not use negative exponents in the answer. Assume that even roots
are of nonnegative quantities.
4
1
4 5  43
Multiply
6q 5 p
Simplify
12x5 y 4
Find a simplified form of f(x). Assume that x can be any real number.
f ( x)  36  x  7 
2
Simplify by taking the roots of the numerator and the denominator. Assume all variables represent positive
numbers.
3
125
27
Divide and, if possible, simplify. Assume all variables represent positive numbers.
48 xy 5
6x
Rationalize the denominator. Assume all variables represent positive numbers.
75
x
Add or subtract. Simplify by combining like radical terms, if possible. Assume all variables and radicands
represent nonnegative numbers.
5 4 x6  6 x 4 x 2
8 3  10 27
Multiply. Assume all variables represent nonnegative numbers.
3

12  3


7 2

5 4

Rationalize the denominator. Assume all variables represent positive numbers.
5 3
5 3
Divide and if possible, simplify. Assume all variables represent positive real numbers
4
3
x
x2
Solve
4x  3  8
3x  4  4 x  3
Find the distance between the pair of points. Give your answer in exact form and where appropriate find an
approximation to three decimal places.
(6, -2) and ( 8, -9)
Find the midpoint of the segment with the given endpoints.
(4, -7) and (-2, 10)
Express in terms of i.
25  81
64
Perform the indicated operation and simplify. Write the answer in the form a + bi.
 4  2i   3  6i 
 4  2i   3  6i 
Find the power of i.
i 32
i 21
4
3i
 4  2i 3  6i 
i 42
i 39
Perform the indicated operation and simplify. Write the answer in the form a + bi.
 3  4i 
2
A diagonal crosswalk at an intersection of State and Main is the hypotenuse of a triangle in which crosswalks
across each street are the legs. State is 32 feet wide and Main is 21 feet wide. How much shorter is the
distance traveled by pedestrians using the diagonal crosswalk rather than using both crosswalks that form the
legs of the triangle.