Question 1

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$- 7 ^ { - 4 }$

Accepted Answer

A)  2401 
B)  $\frac { 1 } { 2401 }$ 
C)  $- 2401$ 
D)  $- \frac { 1 } { 2401 }$ 
A)  2401 
B)  $\frac { 1 } { 2401 }$ 
C)  $- 2401$ 
D)  $- \frac { 1 } { 2401 }$

Question 2

Simplify the expression. Assume all variables represent nonzero real numbers.
-$$( - 2 x ) ^ { 3 }$$

Accepted Answer

A)  $- 8 x ^ { 3 }$ 
B)  $8 x$ 
C)  $- 6 x$ 
D)  $6 \mathrm { x } ^ { 3 }$ 
A)  $- 8 x ^ { 3 }$ 
B)  $8 x$ 
C)  $- 6 x$ 
D)  $6 \mathrm { x } ^ { 3 }$

Question 3

Decide whether the expression has been simplified correctly.
-$6 ^ { 0 } \times = 0$

Accepted Answer

A)  Simplified correctly 
B)  Not simplified correctly 
A)  Simplified correctly 
B)  Not simplified correctly

Question 4

Write in radical form. Assume all variables represent positive real numbers.
-$( - 2 x ) ^ { 1 / 5 }$

Accepted Answer

A)  $\frac { 1 } { \sqrt [ 5 ] { - 2 x } }$ 
B)  $\sqrt { - \frac { 2 x } { 5 } }$ 
C)  $\sqrt [ 5 ] { - 2 x }$ 
D)  $\sqrt [ 1 / 5 ] { - 2 x }$ 
A)  $\frac { 1 } { \sqrt [ 5 ] { - 2 x } }$ 
B)  $\sqrt { - \frac { 2 x } { 5 } }$ 
C)  $\sqrt [ 5 ] { - 2 x }$ 
D)  $\sqrt [ 1 / 5 ] { - 2 x }$

Question 5

Evaluate the expression.
-$256 ^ { 5 / 4 }$

Accepted Answer

A)  16,384 
B)  262,144 
C)  65,536 
D)  1024 
A)  16,384 
B)  262,144 
C)  65,536 
D)  1024

Question 6

Evaluate the expression for x $$x = - 2 , y = 3 , \text { and } a = - 4$$
-$$\frac { - ( x + 5 ) ^ { 2 } - 2 y } { - 2 - a }$$

Accepted Answer

A)  $\frac { 15 } { 2 }$ 
B)  $- \frac { 15 } { 2 }$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $\frac { 35 } { 2 }$ 
A)  $\frac { 15 } { 2 }$ 
B)  $- \frac { 15 } { 2 }$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $\frac { 35 } { 2 }$

Question 7

Write the expression in lowest terms.
-$$\frac { 3 m ^ { 2 } + 20 m + 12 } { 2 m ^ { 2 } + 15 m + 18 }$$

Accepted Answer

A)  $\frac { \mathrm { m } + 3 } { \mathrm {~m} + 4 }$ 
B)  $\frac { 3 m + 6 } { 2 m - 6 }$ 
C)  $\frac { m - 2 } { m - 3 }$ 
D)  $\frac { 3 m + 2 } { 2 m + 3 }$ 
A)  $\frac { \mathrm { m } + 3 } { \mathrm {~m} + 4 }$ 
B)  $\frac { 3 m + 6 } { 2 m - 6 }$ 
C)  $\frac { m - 2 } { m - 3 }$ 
D)  $\frac { 3 m + 2 } { 2 m + 3 }$

Question 8

Find the sum or difference.
-$$\frac { x ^ { 2 } + 5 x - 24 } { x + 8 }$$

Accepted Answer

A)  $x + 3$ 
B)  $x ^ { 2 } - 3$ 
C)  $x ^ { 2 } + 6 x - 16$ 
D)  $x - 3$ 
A)  $x + 3$ 
B)  $x ^ { 2 } - 3$ 
C)  $x ^ { 2 } + 6 x - 16$ 
D)  $x - 3$

Question 9

Provide an appropriate response.
-The formula used to find the volume of the frustum of a square pyramid is $V = \frac { 1 } { 3 } h \left( a ^ { 2 } + a b + b ^ { 2 } \right)$, where $b$ is the length of the base, $a$ is the length of the top, and $h$ is the height. Try to visualize the figure if $a = b = h$. Calculate the volume if $a = 253$ feet, $b = 253$ feet, and $h = 253$ feet.

Accepted Answer

A)  16,195,277 cubic feet 
B)  64,009 cubic feet 
C)  16,194,377 cubic feet 
D)  16,194,277 cubic feet 
A)  16,195,277 cubic feet 
B)  64,009 cubic feet 
C)  16,194,377 cubic feet 
D)  16,194,277 cubic feet

Question 10

Evaluate the expression.
-$$\left( - \frac { 1 } { 1024 } \right) ^ { - 1 / 5 }$$

Accepted Answer

A)  $- \frac { 1 } { 4 }$ 
B)  $- 4$ 
C)  $1,125,899,906,842,624$ 
D)  not a real number 
A)  $- \frac { 1 } { 4 }$ 
B)  $- 4$ 
C)  $1,125,899,906,842,624$ 
D)  not a real number

Question 11

Find the sum or difference.
-$$( 4 x - 2 y + 7 ) ( 4 x - 2 y - 7 )$$

Accepted Answer

A)  $- 16 x y - 28 x + - 14 y - 49$ 
B)  $16 x ^ { 2 } + 16 x y - 4 y ^ { 2 } - 98$ 
C)  $8 x ^ { 2 } - 4 y ^ { 2 } - 98$ 
D)  $16 x ^ { 2 } - 16 x y + 4 y ^ { 2 } - 49$ 
A)  $- 16 x y - 28 x + - 14 y - 49$ 
B)  $16 x ^ { 2 } + 16 x y - 4 y ^ { 2 } - 98$ 
C)  $8 x ^ { 2 } - 4 y ^ { 2 } - 98$ 
D)  $16 x ^ { 2 } - 16 x y + 4 y ^ { 2 } - 49$

Question 12

Factor, using the given factor. Assume all variables represent positive real numbers.
-$4 m ^ { 11 / 4 } - 3 m ^ { - 1 / 2 } ; \quad m ^ { - 1 / 2 }$

Accepted Answer

A)  $m ^ { - 1 / 2 } \left( 12 m ^ { 13 / 4 } - 4 \right)$ 
B) $m^{-1 / 2}(4 m ^{11 / 4}+3)$ 
C) $3 m^{-1 / 4}\left(4 m^{13 / 4}-1\right)$ 
D)  $\mathrm { m } ^ { - 1 / 2 } \left( 4 \mathrm {~m} ^ { 13 / 4 } - 3 \right)$ 
A)  $m ^ { - 1 / 2 } \left( 12 m ^ { 13 / 4 } - 4 \right)$ 
B) $m^{-1 / 2}(4 m ^{11 / 4}+3)$ 
C) $3 m^{-1 / 4}\left(4 m^{13 / 4}-1\right)$ 
D)  $\mathrm { m } ^ { - 1 / 2 } \left( 4 \mathrm {~m} ^ { 13 / 4 } - 3 \right)$

Question 13

Factor by any method.
-$30 x ^ { 2 } + 36 x y + 25 x y + 30 y ^ { 2 }$

Accepted Answer

A)  $( 30 x + 5 y ) ( x + 6 y )$ 
B)  $( 6 x - 5 y ) ( 5 x + 6 y )$ 
C)  $( 6 x + 5 ) ( 5 x + 6 )$ 
D)  $( 6 x + 5 y ) ( 5 x + 6 y )$ 
A)  $( 30 x + 5 y ) ( x + 6 y )$ 
B)  $( 6 x - 5 y ) ( 5 x + 6 y )$ 
C)  $( 6 x + 5 ) ( 5 x + 6 )$ 
D)  $( 6 x + 5 y ) ( 5 x + 6 y )$

Question 14

Identify the expression as a polynomial or not a polynomial.
-$- 9$

Accepted Answer

A)  Polynomial 
B)  Not a polynomial 
A)  Polynomial 
B)  Not a polynomial

Question 15

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$\frac { \frac { 4 } { y } } { y + 4 }$

Accepted Answer

A)  $24 y ( y + 4 )$ 
B)  $\frac { y + 4 } { 24 y }$ 
C)  $\frac { 2 ( y + 4 ) } { 3 y }$ 
D)  $\frac { 3 y } { 2 ( y + 4 ) }$ 
A)  $24 y ( y + 4 )$ 
B)  $\frac { y + 4 } { 24 y }$ 
C)  $\frac { 2 ( y + 4 ) } { 3 y }$ 
D)  $\frac { 3 y } { 2 ( y + 4 ) }$

Question 16

Write the expression in lowest terms.
-$$\frac { x ^ { 3 } + 125 } { x + 5 }$$

Accepted Answer

A)  $x ^ { 2 } + 25$ 
B)  $x ^ { 2 } - 5 x + 25$ 
C)  $x ^ { 2 } - 25 x + 5$ 
D)  $x ^ { 2 } - 5$ 
A)  $x ^ { 2 } + 25$ 
B)  $x ^ { 2 } - 5 x + 25$ 
C)  $x ^ { 2 } - 25 x + 5$ 
D)  $x ^ { 2 } - 5$

Question 17

Find the sum or difference.
-$$( n + 7 ) ^ { 2 }$$

Accepted Answer

A)  $n ^ { 2 } + 49$ 
B)  $49 n ^ { 2 } + 14 n + 49$ 
C)  $n + 49$ 
D)  $n ^ { 2 } + 14 n + 49$ 
A)  $n ^ { 2 } + 49$ 
B)  $49 n ^ { 2 } + 14 n + 49$ 
C)  $n + 49$ 
D)  $n ^ { 2 } + 14 n + 49$

Question 18

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { \frac { 18 } { x } }$

Accepted Answer

A)  $\frac { \sqrt { 3 x } } { x }$ 
B)  $\frac { 3 \sqrt { 2 x } } { x }$ 
C)  $3 \sqrt { 2 x }$ 
D)  $3 \sqrt { \frac { 2 } { x } }$ 
A)  $\frac { \sqrt { 3 x } } { x }$ 
B)  $\frac { 3 \sqrt { 2 x } } { x }$ 
C)  $3 \sqrt { 2 x }$ 
D)  $3 \sqrt { \frac { 2 } { x } }$

Question 19

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-When determining appropriate doses of medication, it is sometimes important to estimate the body surface area (BSA) of a patient. This surface area (in $\mathrm { m } ^ { 2 }$ ) can be approximated using the Mosteller formula
$$\mathrm { BSA } = \left( \frac { \mathrm { h } \cdot \mathrm { w } } { 3600 } \right) ^ { 1 / 2 } ,$$
where $h$ is the patient's height in centimeters and $w$ is the weight in kilograms. Determine the BSA for a patient v height $182 \mathrm {~cm}$ and weight $63 \mathrm {~kg}$. Round your answer to two decimal places.

Accepted Answer

A)  $10.14 \mathrm {~m} ^ { 2 }$ 
B)  $0.03 \mathrm {~m} ^ { 2 }$ 
C)  $3.19 \mathrm {~m} ^ { 2 }$ 
D)  $1.78 \mathrm {~m} ^ { 2 }$ 
A)  $10.14 \mathrm {~m} ^ { 2 }$ 
B)  $0.03 \mathrm {~m} ^ { 2 }$ 
C)  $3.19 \mathrm {~m} ^ { 2 }$ 
D)  $1.78 \mathrm {~m} ^ { 2 }$

Question 20

Factor by any method.
-$$t ^ { 3 } + 512$$

Accepted Answer

A)  $( t - 512 ) \left( t ^ { 2 } - 1 \right)$ 
B)  $( t + 8 ) \left( t ^ { 2 } + 64 \right)$ 
C)  $( t - 8 ) \left( t ^ { 2 } + 8 t + 64 \right)$ 
D)  $( t + 8 ) \left( t ^ { 2 } - 8 t + 64 \right)$ 
A)  $( t - 512 ) \left( t ^ { 2 } - 1 \right)$ 
B)  $( t + 8 ) \left( t ^ { 2 } + 64 \right)$ 
C)  $( t - 8 ) \left( t ^ { 2 } + 8 t + 64 \right)$ 
D)  $( t + 8 ) \left( t ^ { 2 } - 8 t + 64 \right)$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- 7 ^ { - 4 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $( - 2 x ) ^ { 3 }$

Decide whether the expression has been simplified correctly. - $6 ^ { 0 } \times = 0$

Write in radical form. Assume all variables represent positive real numbers. - $( - 2 x ) ^ { 1 / 5 }$

Evaluate the expression. - $256 ^ { 5 / 4 }$

Evaluate the expression for x $x = - 2 , y = 3 , \text { and } a = - 4$ - $\frac { - ( x + 5 ) ^ { 2 } - 2 y } { - 2 - a }$

Write the expression in lowest terms. - $\frac { 3 m ^ { 2 } + 20 m + 12 } { 2 m ^ { 2 } + 15 m + 18 }$

Find the sum or difference. - $\frac { x ^ { 2 } + 5 x - 24 } { x + 8 }$

Evaluate the expression. - $\left( - \frac { 1 } { 1024 } \right) ^ { - 1 / 5 }$

Find the sum or difference. - $( 4 x - 2 y + 7 ) ( 4 x - 2 y - 7 )$

Factor, using the given factor. Assume all variables represent positive real numbers. - $4 m ^ { 11 / 4 } - 3 m ^ { - 1 / 2 } ; \quad m ^ { - 1 / 2 }$

Factor by any method. - $30 x ^ { 2 } + 36 x y + 25 x y + 30 y ^ { 2 }$

Identify the expression as a polynomial or not a polynomial. - $- 9$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { 4 } { y } } { y + 4 }$

Write the expression in lowest terms. - $\frac { x ^ { 3 } + 125 } { x + 5 }$

Find the sum or difference. - $( n + 7 ) ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 18 } { x } }$

Factor by any method. - $t ^ { 3 } + 512$

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Exam 1: Review of Basic Concepts

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - −7−4- 7 ^ { - 4 }−7−4

Simplify the expression. Assume all variables represent nonzero real numbers. - (−2x)3( - 2 x ) ^ { 3 }(−2x)3

Decide whether the expression has been simplified correctly. - 60×=06 ^ { 0 } \times = 060×=0

Write in radical form. Assume all variables represent positive real numbers. - (−2x)1/5( - 2 x ) ^ { 1 / 5 }(−2x)1/5

Evaluate the expression. - 2565/4256 ^ { 5 / 4 }2565/4

Evaluate the expression for x x=−2,y=3, and a=−4x = - 2 , y = 3 , \text { and } a = - 4x=−2,y=3, and a=−4 - −(x+5)2−2y−2−a\frac { - ( x + 5 ) ^ { 2 } - 2 y } { - 2 - a }−2−a−(x+5)2−2y​

Write the expression in lowest terms. - 3m2+20m+122m2+15m+18\frac { 3 m ^ { 2 } + 20 m + 12 } { 2 m ^ { 2 } + 15 m + 18 }2m2+15m+183m2+20m+12​

Find the sum or difference. - x2+5x−24x+8\frac { x ^ { 2 } + 5 x - 24 } { x + 8 }x+8x2+5x−24​

Evaluate the expression. - (−11024)−1/5\left( - \frac { 1 } { 1024 } \right) ^ { - 1 / 5 }(−10241​)−1/5

Find the sum or difference. - (4x−2y+7)(4x−2y−7)( 4 x - 2 y + 7 ) ( 4 x - 2 y - 7 )(4x−2y+7)(4x−2y−7)

Factor, using the given factor. Assume all variables represent positive real numbers. - 4m11/4−3m−1/2;m−1/24 m ^ { 11 / 4 } - 3 m ^ { - 1 / 2 } ; \quad m ^ { - 1 / 2 }4m11/4−3m−1/2;m−1/2

Factor by any method. - 30x2+36xy+25xy+30y230 x ^ { 2 } + 36 x y + 25 x y + 30 y ^ { 2 }30x2+36xy+25xy+30y2

Identify the expression as a polynomial or not a polynomial. - −9- 9−9

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 4yy+4\frac { \frac { 4 } { y } } { y + 4 }y+4y4​​

Write the expression in lowest terms. - x3+125x+5\frac { x ^ { 3 } + 125 } { x + 5 }x+5x3+125​

Find the sum or difference. - (n+7)2( n + 7 ) ^ { 2 }(n+7)2

Simplify the expression. Assume all variables represent positive real numbers. - 18x\sqrt { \frac { 18 } { x } }x18​​

Factor by any method. - t3+512t ^ { 3 } + 512t3+512