Question 1

Write in radical form. Assume all variables represent positive real numbers.
-$$( 9 m + n ) ^ { 3 / 4 }$$

Accepted Answer

A)  $\sqrt [ 4 ] { ( 9 m + n ) ^ { 3 } }$ 
B)  $\sqrt [ 4 ] { 9 m + n ^ { 3 } }$ 
C)  $\sqrt [ 3 ] { ( 9 m + n ) ^ { 4 } }$ 
D)  $\sqrt [ 3 ] { 9 m + n ^ { 4 } }$ 
A)  $\sqrt [ 4 ] { ( 9 m + n ) ^ { 3 } }$ 
B)  $\sqrt [ 4 ] { 9 m + n ^ { 3 } }$ 
C)  $\sqrt [ 3 ] { ( 9 m + n ) ^ { 4 } }$ 
D)  $\sqrt [ 3 ] { 9 m + n ^ { 4 } }$

Question 2

Find the product. Assume variables represent positive real numbers.
-$\left( - 7 p ^ { 3 / 5 } + 2 p ^ { 4 / 5 } \right) ^ { 2 }$

Accepted Answer

A)  $49 p ^ { 6 / 5 } - 14 p ^ { 7 / 5 } + 4 p ^ { 8 / 5 }$ 
B)  $49 p ^ { 6 / 5 } - 28 p ^ { 7 / 5 } + 4 p ^ { 8 / 5 }$ 
C)  $- 14 p ^ { 6 / 5 } - 14 p ^ { 4 / 5 } + 4 p ^ { 8 / 5 }$ 
D)  $49 \mathrm { p } ^ { 9 / 25 } + 7 \mathrm { p }$ 
A)  $49 p ^ { 6 / 5 } - 14 p ^ { 7 / 5 } + 4 p ^ { 8 / 5 }$ 
B)  $49 p ^ { 6 / 5 } - 28 p ^ { 7 / 5 } + 4 p ^ { 8 / 5 }$ 
C)  $- 14 p ^ { 6 / 5 } - 14 p ^ { 4 / 5 } + 4 p ^ { 8 / 5 }$ 
D)  $49 \mathrm { p } ^ { 9 / 25 } + 7 \mathrm { p }$

Question 3

Provide an appropriate response.
-The number of farms in a certain country since 1940, in millions, can be approximated by evaluating the polynomial $0.000026045689 x ^ { 3 } - 0.1522580959 x ^ { 2 } + 296.5669762 x - 192,464.713$, where $x$ is the year in question. Evaluate the polynomial for $x = 2000$ to determine the number of farms in 2000 . Round the answer to the nearest million farms.

Accepted Answer

A)  5 million farms 
B)  4 million farms 
C)  1 million farms 
D)  2 million farms 
A)  5 million farms 
B)  4 million farms 
C)  1 million farms 
D)  2 million farms

Question 4

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\left( 16 \mathrm { k } ^ { 4 } \mathrm {~m} ^ { - 8 } \right) ^ { 1 / 4 }$$

Accepted Answer

A)  $\frac { 4 k } { m ^ { 2 } }$ 
B)  $4 \mathrm {~km} ^ { 2 }$ 
C)  $\frac { 2 k } { m ^ { 2 } }$ 
D)  $2 \mathrm {~km} ^ { 2 }$ 
A)  $\frac { 4 k } { m ^ { 2 } }$ 
B)  $4 \mathrm {~km} ^ { 2 }$ 
C)  $\frac { 2 k } { m ^ { 2 } }$ 
D)  $2 \mathrm {~km} ^ { 2 }$

Question 5

Determine the degree of the polynomial.
-$2 x ^ { 6 } - 8 x ^ { 7 } + 9 x ^ { 2 } - 7$

Accepted Answer

A)  7 
B)  15 
C)  4 
D)  6 
A)  7 
B)  15 
C)  4 
D)  6

Question 6

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

Accepted Answer

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

Question 7

Factor, using the given factor. Assume all variables represent positive real numbers.
-$15 y ^ { 4 } ( 2 y + 1 ) ^ { - 2 / 5 } + 20 y ^ { 3 } ( 2 y + 1 ) ^ { 3 / 5 } - 40 y ^ { 2 } ( 2 y + 1 ) ^ { 8 / 5 } ; \quad 5 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 }$

Accepted Answer

A)  $5 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( - 21 y ^ { 2 } - 28 y - 8 \right)$ 
B)  $5 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( 21 y ^ { 2 } - 28 y + 8 \right)$ 
C)  $5 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( 19 y ^ { 2 } - 28 y + 8 \right)$ 
D)  $5 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( - 19 y ^ { 2 } - 28 y - 8 \right)$ 
A)  $5 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( - 21 y ^ { 2 } - 28 y - 8 \right)$ 
B)  $5 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( 21 y ^ { 2 } - 28 y + 8 \right)$ 
C)  $5 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( 19 y ^ { 2 } - 28 y + 8 \right)$ 
D)  $5 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 } \left( - 19 y ^ { 2 } - 28 y - 8 \right)$

Question 8

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$\frac { 5 ^ { - 8 } } { 5 ^ { 6 } }$

Accepted Answer

A)  $\frac { 1 } { 5^{48} }$ 
B)  $- 5^{14}$ 
C)  $\frac { 1 } { 5^{14 }}$ 
D)  $\frac { 1 } { 10 ^ { 14 } }$ 
A)  $\frac { 1 } { 5^{48} }$ 
B)  $- 5^{14}$ 
C)  $\frac { 1 } { 5^{14 }}$ 
D)  $\frac { 1 } { 10 ^ { 14 } }$

Question 9

Factor the trinomial, if possible.
-$14 x ^ { 2 } - 49 x - 28$

Accepted Answer

A)  $( 14 x - 7 ) ( x + 4 )$ 
B)  $( 2 x - 1 ) ( 7 x + 28 )$ 
C)  $7 ( 2 x - 1 ) ( x + 4 )$ 
D)  $7 ( 2 x + 1 ) ( x - 4 )$ 
A)  $( 14 x - 7 ) ( x + 4 )$ 
B)  $( 2 x - 1 ) ( 7 x + 28 )$ 
C)  $7 ( 2 x - 1 ) ( x + 4 )$ 
D)  $7 ( 2 x + 1 ) ( x - 4 )$

Question 10

Factor the polynomial by substitution.
-$$10 ( p + 3 ) ^ { 2 } + 31 ( p + 3 ) + 15$$

Accepted Answer

A)  $( 2 p + 5 ) ( 5 p + 3 )$ 
B)  $( 2 p + 8 ) ( 5 p + 6 )$ 
C)  $( 2 p + 11 ) ( 5 p + 18 )$ 
D)  $( 2 p + 9 ) ( 5 p + 20 )$ 
A)  $( 2 p + 5 ) ( 5 p + 3 )$ 
B)  $( 2 p + 8 ) ( 5 p + 6 )$ 
C)  $( 2 p + 11 ) ( 5 p + 18 )$ 
D)  $( 2 p + 9 ) ( 5 p + 20 )$

Question 11

Solve the problem.
-If the radius of a sphere is doubled, by what factor will the volume change?

Accepted Answer

A)  6 
B)  2 
C)  8 
D)  4 
A)  6 
B)  2 
C)  8 
D)  4

Question 12

Evaluate the expression.
-$$\left( 7 - 6 ^ { 2 } \right) ( - 6 + \sqrt { 100 } )$$

Accepted Answer

A)  $- 20$ 
B)  $- 3074$ 
C)  94 
D)  -116 
A)  $- 20$ 
B)  $- 3074$ 
C)  94 
D)  -116

Question 13

Factor by any method.
-$16 x ^ { 2 } + 40 x + 25 - y ^ { 2 }$

Accepted Answer

A)  $( 4 x - 5 + y ) ( 4 x - 5 - y )$ 
B)  $( 4 x + 5 + y ) ( 4 x - 5 - y )$ 
C)  $( 4 x + 5 + y ) ( 4 x + 5 - y )$ 
D)  prime 
A)  $( 4 x - 5 + y ) ( 4 x - 5 - y )$ 
B)  $( 4 x + 5 + y ) ( 4 x - 5 - y )$ 
C)  $( 4 x + 5 + y ) ( 4 x + 5 - y )$ 
D)  prime

Question 14

Factor the trinomial, if possible.
-$$- 2 x ^ { 3 } - 6 x ^ { 2 } + 56 x$$

Accepted Answer

A)  $- 2 x ( x + 4 ) ( x - 7 )$ 
B)  $- 2 x ^ { 2 } ( x - 4 ) ( x - 7 )$ 
C)  $2 x ( x + 4 ) ( x + 7 )$ 
D)  $- 2 x ( x - 4 ) ( x + 7 )$ 
A)  $- 2 x ( x + 4 ) ( x - 7 )$ 
B)  $- 2 x ^ { 2 } ( x - 4 ) ( x - 7 )$ 
C)  $2 x ( x + 4 ) ( x + 7 )$ 
D)  $- 2 x ( x - 4 ) ( x + 7 )$

Question 15

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

Accepted Answer

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

Question 16

Factor by any method.
-$$15 ( m - 2 ) ^ { 2 } - 13 ( m - 2 ) - 6$$

Accepted Answer

A)  $( 5 \mathrm {~m} + 11 ) ( 3 \mathrm {~m} + 12 )$ 
B)  $( 5 m - 16 ) ( 3 m - 5 )$ 
C)  $( 5 m + 8 ) ( 3 m + 3 )$ 
D)  $( 5 m + 6 ) ( 3 m + 1 )$ 
A)  $( 5 \mathrm {~m} + 11 ) ( 3 \mathrm {~m} + 12 )$ 
B)  $( 5 m - 16 ) ( 3 m - 5 )$ 
C)  $( 5 m + 8 ) ( 3 m + 3 )$ 
D)  $( 5 m + 6 ) ( 3 m + 1 )$

Question 17

Factor the trinomial, if possible.
-$$9 m ^ { 2 } + 18 m + 9$$

Accepted Answer

A)  $( 3 m - 2 ) ^ { 2 }$ 
B)  $( 3 m + 2 ) ^ { 2 }$ 
C)  $9 ( \mathrm {~m} + 1 ) ^ { 2 }$ 
D)  $9 ( m - 1 ) ^ { 2 }$ 
A)  $( 3 m - 2 ) ^ { 2 }$ 
B)  $( 3 m + 2 ) ^ { 2 }$ 
C)  $9 ( \mathrm {~m} + 1 ) ^ { 2 }$ 
D)  $9 ( m - 1 ) ^ { 2 }$

Question 18

Find the product.
-$$( 2 x + 2 ) ( x - 3 )$$

Accepted Answer

A)  $x ^ { 2 } - 6 x - 4$ 
B)  $2 x ^ { 2 } - 5 x - 6$ 
C)  $2 x ^ { 2 } - 4 x - 6$ 
D)  $x ^ { 2 } - 4 x - 5$ 
A)  $x ^ { 2 } - 6 x - 4$ 
B)  $2 x ^ { 2 } - 5 x - 6$ 
C)  $2 x ^ { 2 } - 4 x - 6$ 
D)  $x ^ { 2 } - 4 x - 5$

Question 19

Evaluate the expression.
-$$7 + 4 ^ { 2 } - ( - 10 ) \cdot 5$$

Accepted Answer

A)  $- 27$ 
B)  73 
C)  65 
D)  125 
A)  $- 27$ 
B)  73 
C)  65 
D)  125

Question 20

Perform the indicated operations.
-$$\frac { 8 } { 2 r ^ { 2 } - 5 r s - 3 s ^ { 2 } } - \frac { 8 } { 5 r ^ { 2 } - 16 r s + 3 s ^ { 2 } } + \frac { 7 } { 10 r ^ { 2 } + 3 r s - s ^ { 2 } }$$

Accepted Answer

A)  $\frac { 63 r - 37 s } { ( 2 r + s ) ( r - 3 s ) ( 5 r - s ) }$ 
B)  $\frac { 63 r - 21 s } { ( 2 r + s ) ( r - 3 s ) ( 5 r - s ) }$ 
C)  $\frac { 31 r - 21 s } { ( 2 r + s ) ( r - 3 s ) ( 5 r - s ) }$ 
D)  $\frac { 31 r - 37 s } { ( 2 r + s ) ( r - 3 s ) ( 5 r - s ) }$ 
A)  $\frac { 63 r - 37 s } { ( 2 r + s ) ( r - 3 s ) ( 5 r - s ) }$ 
B)  $\frac { 63 r - 21 s } { ( 2 r + s ) ( r - 3 s ) ( 5 r - s ) }$ 
C)  $\frac { 31 r - 21 s } { ( 2 r + s ) ( r - 3 s ) ( 5 r - s ) }$ 
D)  $\frac { 31 r - 37 s } { ( 2 r + s ) ( r - 3 s ) ( 5 r - s ) }$

Write in radical form. Assume all variables represent positive real numbers. - $( 9 m + n ) ^ { 3 / 4 }$

Find the product. Assume variables represent positive real numbers. - $\left( - 7 p ^ { 3 / 5 } + 2 p ^ { 4 / 5 } \right) ^ { 2 }$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\left( 16 \mathrm { k } ^ { 4 } \mathrm {~m} ^ { - 8 } \right) ^ { 1 / 4 }$

Determine the degree of the polynomial. - $2 x ^ { 6 } - 8 x ^ { 7 } + 9 x ^ { 2 } - 7$

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

Factor, using the given factor. Assume all variables represent positive real numbers. - $15 y ^ { 4 } ( 2 y + 1 ) ^ { - 2 / 5 } + 20 y ^ { 3 } ( 2 y + 1 ) ^ { 3 / 5 } - 40 y ^ { 2 } ( 2 y + 1 ) ^ { 8 / 5 } ; \quad 5 y ^ { 2 } ( 2 y + 1 ) ^ { - 2 / 5 }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 5 ^ { - 8 } } { 5 ^ { 6 } }$

Factor the trinomial, if possible. - $14 x ^ { 2 } - 49 x - 28$

Factor the polynomial by substitution. - $10 ( p + 3 ) ^ { 2 } + 31 ( p + 3 ) + 15$

Solve the problem. -If the radius of a sphere is doubled, by what factor will the volume change?

Evaluate the expression. - $\left( 7 - 6 ^ { 2 } \right) ( - 6 + \sqrt { 100 } )$

Factor by any method. - $16 x ^ { 2 } + 40 x + 25 - y ^ { 2 }$

Factor the trinomial, if possible. - $- 2 x ^ { 3 } - 6 x ^ { 2 } + 56 x$

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

Factor by any method. - $15 ( m - 2 ) ^ { 2 } - 13 ( m - 2 ) - 6$

Factor the trinomial, if possible. - $9 m ^ { 2 } + 18 m + 9$

Find the product. - $( 2 x + 2 ) ( x - 3 )$

Evaluate the expression. - $7 + 4 ^ { 2 } - ( - 10 ) \cdot 5$

Perform the indicated operations. - $\frac { 8 } { 2 r ^ { 2 } - 5 r s - 3 s ^ { 2 } } - \frac { 8 } { 5 r ^ { 2 } - 16 r s + 3 s ^ { 2 } } + \frac { 7 } { 10 r ^ { 2 } + 3 r s - s ^ { 2 } }$

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Exam 12: Review of Basic Concepts

Write in radical form. Assume all variables represent positive real numbers. - (9m+n)3/4( 9 m + n ) ^ { 3 / 4 }(9m+n)3/4

Find the product. Assume variables represent positive real numbers. - (−7p3/5+2p4/5)2\left( - 7 p ^ { 3 / 5 } + 2 p ^ { 4 / 5 } \right) ^ { 2 }(−7p3/5+2p4/5)2

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - (16k4 m−8)1/4\left( 16 \mathrm { k } ^ { 4 } \mathrm {~m} ^ { - 8 } \right) ^ { 1 / 4 }(16k4 m−8)1/4

Determine the degree of the polynomial. - 2x6−8x7+9x2−72 x ^ { 6 } - 8 x ^ { 7 } + 9 x ^ { 2 } - 72x6−8x7+9x2−7

Write the expression in lowest terms. - m3−125m−5\frac { m ^ { 3 } - 125 } { m - 5 }m−5m3−125​

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - 5−856\frac { 5 ^ { - 8 } } { 5 ^ { 6 } }565−8​

Factor the trinomial, if possible. - 14x2−49x−2814 x ^ { 2 } - 49 x - 2814x2−49x−28

Factor the polynomial by substitution. - 10(p+3)2+31(p+3)+1510 ( p + 3 ) ^ { 2 } + 31 ( p + 3 ) + 1510(p+3)2+31(p+3)+15