Question 1

Perform the division. $$\frac { - 9 a ^ { 2 } b ^ { 2 } - 6 a ^ { 2 } b - 9 a b ^ { 2 } } { - 3 a b }$$

Accepted Answer

A)  $4 a b + 3 a + 3 b$ 
B)  $4 a b + 2 a + 3 b$ 
C)  $3 a b + 3 a + 3 b$ 
D)  $3 a b + 2 a + 4 b$ 
E)  $3 a b + 2 a + 3 b$ 
A)  $4 a b + 3 a + 3 b$ 
B)  $4 a b + 2 a + 3 b$ 
C)  $3 a b + 3 a + 3 b$ 
D)  $3 a b + 2 a + 4 b$ 
E)  $3 a b + 2 a + 3 b$

Question 2

Find the product. $\left( 3 t ^ { 6 } z ^ { 6 } \right) \left( 2 t ^ { 2 } z ^ { 2 } \right)$

Accepted Answer

A)  $8 t ^ { 9 } z ^ { 9 }$ 
B)  $6 t ^ { 8 } z$ 
C)  $6 t ^ { 4 } z ^ { 4 }$ 
D)  $6 t ^ { 12 } z ^ { 12 }$ 
E)  $5 t ^ { 8 } z$ 
A)  $8 t ^ { 9 } z ^ { 9 }$ 
B)  $6 t ^ { 8 } z$ 
C)  $6 t ^ { 4 } z ^ { 4 }$ 
D)  $6 t ^ { 12 } z ^ { 12 }$ 
E)  $5 t ^ { 8 } z$

Question 3

Simplify the following expression. Assume that $$y \neq 0$$ . $$\frac { 8 y ^ { 4 } \cdot y ^ { 6 } \cdot y ^ { 6 } } { 2 \left( y ^ { 4 } \right) ^ { 3 } }$$

Accepted Answer

A)  $4 y ^ { 137 }$ 
B)  $4 y ^ { 4 }$ 
C)  $6 y ^ { 4 }$ 
D)  $4 y ^ { 9 }$ 
E)  $8 y ^ { 4 }$ 
A)  $4 y ^ { 137 }$ 
B)  $4 y ^ { 4 }$ 
C)  $6 y ^ { 4 }$ 
D)  $4 y ^ { 9 }$ 
E)  $8 y ^ { 4 }$

Question 4

Solve the formula $V = 3 ( r - I ) a$ for the variable $r$ .

Accepted Answer

A)  $r = \frac { 3 V } { a } - 1$ 
B)  $r=\frac{V+1}{3 a}$ 
C)  $r= \frac { V } { 3 a } - 1$ 
D)  $r = \frac { 3 V } { a } + 1$ 
E)  $r = \frac { V } { 3 a } + 1$ 
A)  $r = \frac { 3 V } { a } - 1$ 
B)  $r=\frac{V+1}{3 a}$ 
C)  $r= \frac { V } { 3 a } - 1$ 
D)  $r = \frac { 3 V } { a } + 1$ 
E)  $r = \frac { V } { 3 a } + 1$

Question 5

Write the polynomial with the exponents on x in descending order. $a ^ { 2 } x - a x ^ { 3 } + 2 a ^ { 3 } x ^ { 5 } - 3 a ^ { 3 } x ^ { 2 }$

Accepted Answer

A)  $a ^ { 2 } x - a x ^ { 3 } - 3 a ^ { 3 } x ^ { 2 } + 2 a ^ { 3 } x ^ { 5 }$ 
B)  $a ^ { 2 } x - a x ^ { 3 } + 2 a ^ { 3 } x ^ { 5 } - 3 a ^ { 3 } x ^ { 2 }$ 
C)  $2 a ^ { 3 } x ^ { 5 } - a x ^ { 3 } - 3 a ^ { 3 } x ^ { 2 } + a ^ { 2 } x$ 
D)  $2 a ^ { 3 } x ^ { 5 } - 3 a ^ { 3 } x ^ { 2 } - a x ^ { 3 } + a ^ { 2 } x$ 
E)  $a ^ { 2 } x - 3 a ^ { 3 } x ^ { 2 } - a x ^ { 3 } + 2 a ^ { 3 } x ^ { 5 }$ 
A)  $a ^ { 2 } x - a x ^ { 3 } - 3 a ^ { 3 } x ^ { 2 } + 2 a ^ { 3 } x ^ { 5 }$ 
B)  $a ^ { 2 } x - a x ^ { 3 } + 2 a ^ { 3 } x ^ { 5 } - 3 a ^ { 3 } x ^ { 2 }$ 
C)  $2 a ^ { 3 } x ^ { 5 } - a x ^ { 3 } - 3 a ^ { 3 } x ^ { 2 } + a ^ { 2 } x$ 
D)  $2 a ^ { 3 } x ^ { 5 } - 3 a ^ { 3 } x ^ { 2 } - a x ^ { 3 } + a ^ { 2 } x$ 
E)  $a ^ { 2 } x - 3 a ^ { 3 } x ^ { 2 } - a x ^ { 3 } + 2 a ^ { 3 } x ^ { 5 }$

Question 6

Subtract. $$\begin{array} { r } 
6 x ^ { 2 } - 6 x + 6 \
3 x ^ { 2 } - 3 x - 5\
\hline 
\end{array}$$

Accepted Answer

A)  $3 x ^ { 2 } - 3 x + 11$ 
B)  $3 x ^ { 2 } - 3 x - 1$ 
C)  $6 x ^ { 2 } - 3 x + 1$ 
D)  $3 x ^ { 2 } - 3 x + 1$ 
E)  $6 x ^ { 2 } - 3 x + 11$ 
A)  $3 x ^ { 2 } - 3 x + 11$ 
B)  $3 x ^ { 2 } - 3 x - 1$ 
C)  $6 x ^ { 2 } - 3 x + 1$ 
D)  $3 x ^ { 2 } - 3 x + 1$ 
E)  $6 x ^ { 2 } - 3 x + 11$

Question 7

Evaluate $- x ^ { 2 } - 4$ for $x = - 1$ .

Accepted Answer

A) -7 
B) -4 
C) 5 
D) -3 
E) -5 
A) -7 
B) -4 
C) 5 
D) -3 
E) -5

Question 8

Find the quotient. $$\frac { 12 x ^ { 7 } y ^ { 9 } } { - 6 x ^ { 5 } y ^ { 4 } }$$

Accepted Answer

A)  $- x ^ { 12 } y ^ { 13 }$ 
B)  $- 2 x ^ { 12 } y ^ { 13 }$ 
C)  $- 2 x ^ { 2 } y ^ { 13 }$ 
D)  $- x ^ { 12 } y ^ { 5 }$ 
E)  $- 2 x ^ { 2 } y ^ { 5 }$ 
A)  $- x ^ { 12 } y ^ { 13 }$ 
B)  $- 2 x ^ { 12 } y ^ { 13 }$ 
C)  $- 2 x ^ { 2 } y ^ { 13 }$ 
D)  $- x ^ { 12 } y ^ { 5 }$ 
E)  $- 2 x ^ { 2 } y ^ { 5 }$

Question 9

Find the indicated product by applying the distributive property and combining similar terms. $$\left( x ^ { 2 } - 7 x - 6 \right) \left( x ^ { 2 } + 9 x - 9 \right)$$

Accepted Answer

A)  $x ^ { 4 } + 2 x ^ { 3 } - 15 x ^ { 2 } + 54 x + 9$ 
B)  $x ^ { 4 } + 2 x ^ { 3 } - 78 x ^ { 2 } + 9 x + 54$ 
C)  $x ^ { 4 } - 2 x ^ { 3 } - 72 x ^ { 2 } + 9 x + 54$ 
D)  $x ^ { 4 } + 2 x ^ { 3 } - 78 x ^ { 2 } + 9 x - 54$ 
E)  $x ^ { 4 } + 2 x ^ { 3 } - 78 x ^ { 2 } + 63 x + 54$ 
A)  $x ^ { 4 } + 2 x ^ { 3 } - 15 x ^ { 2 } + 54 x + 9$ 
B)  $x ^ { 4 } + 2 x ^ { 3 } - 78 x ^ { 2 } + 9 x + 54$ 
C)  $x ^ { 4 } - 2 x ^ { 3 } - 72 x ^ { 2 } + 9 x + 54$ 
D)  $x ^ { 4 } + 2 x ^ { 3 } - 78 x ^ { 2 } + 9 x - 54$ 
E)  $x ^ { 4 } + 2 x ^ { 3 } - 78 x ^ { 2 } + 63 x + 54$

Question 10

Perform the division. $$\frac { 20 a ^ { 6 } b ^ { 5 } - 12 a ^ { 5 } b ^ { 6 } } { 4 a ^ { 5 } b ^ { 5 } }$$

Accepted Answer

A)  $5 b - 3 a$ 
B)  $2 a - 7 b$ 
C)  $5 a - 3 b$ 
D)  $5 b - 4 a$ 
E)  $2 a ^ { 2 } - 7 b$ 
A)  $5 b - 3 a$ 
B)  $2 a - 7 b$ 
C)  $5 a - 3 b$ 
D)  $5 b - 4 a$ 
E)  $2 a ^ { 2 } - 7 b$

Question 11

Simplify the following expression. $$\left( \frac { 9 } { 16 } \right) ^ { - 1 }$$

Accepted Answer

A)  $\frac { 9 } { 16 }$ 
B)  $- \frac { 9 } { 16 }$ 
C) 1 
D)  $\frac { 16 } { 9 }$ 
E)  $- \frac { 16 } { 9 }$ 
A)  $\frac { 9 } { 16 }$ 
B)  $- \frac { 9 } { 16 }$ 
C) 1 
D)  $\frac { 16 } { 9 }$ 
E)  $- \frac { 16 } { 9 }$

Question 12

Find the product. $\left( 2 s ^ { 5 } x ^ { 5 } \right) \left( 3 s ^ { 2 } x ^ { 3 } \right) ( s x )$

Accepted Answer

A)  $5 s ^ { 7 } x ^ { 8 }$ 
B)  $6 s ^ { 8 } x ^ { 9 }$ 
C)  $6 s ^ { 10 } x ^ { 15 }$ 
D)  $6 s ^ { 3 } x ^ { 2 }$ 
E) none of these 
A)  $5 s ^ { 7 } x ^ { 8 }$ 
B)  $6 s ^ { 8 } x ^ { 9 }$ 
C)  $6 s ^ { 10 } x ^ { 15 }$ 
D)  $6 s ^ { 3 } x ^ { 2 }$ 
E) none of these

Question 13

Write the number $( 2.15 ) ( 10 ) ^ { 4 }$ in ordinary decimal notation. For example (2.78)(10) 4 = 27,800.

Accepted Answer

A) 215,000 
B) 2,150,000 
C) 2,150 
D) 215 
E) 21,500 
A) 215,000 
B) 2,150,000 
C) 2,150 
D) 215 
E) 21,500

Question 14

Find the product. $$( 4 a + t ) ^ { 2 }$$

Accepted Answer

A)  $16 a ^ { 2 } + 8 a t + t ^ { 2 }$ 
B)  $22 a ^ { 2 } + 16 a t + t ^ { 2 }$ 
C)  $24 a ^ { 2 } + 10 a t + t ^ { 2 }$ 
D)  $19 a ^ { 2 } + 11 a t + t ^ { 2 }$ 
E)  $25 a ^ { 2 } + 13 a t + t ^ { 2 }$ 
A)  $16 a ^ { 2 } + 8 a t + t ^ { 2 }$ 
B)  $22 a ^ { 2 } + 16 a t + t ^ { 2 }$ 
C)  $24 a ^ { 2 } + 10 a t + t ^ { 2 }$ 
D)  $19 a ^ { 2 } + 11 a t + t ^ { 2 }$ 
E)  $25 a ^ { 2 } + 13 a t + t ^ { 2 }$

Question 15

Write the following expression without using a negative exponent. $( - 32 ) ^ { - 1 }$

Accepted Answer

A) 1 
B) 32 
C)  $- \frac { 1 } { 32 }$ 
D) -32 
E)  $\frac { 1 } { 32 }$ 
A) 1 
B) 32 
C)  $- \frac { 1 } { 32 }$ 
D) -32 
E)  $\frac { 1 } { 32 }$

Question 16

Simplify the expression. 3 y ( xy + y )- 5 y  2( x - 2 + 3 y )+ 2( y  3 + y  2)

Accepted Answer

A) - 2 xy  2 + 13 y  2 + 12 y  3 
B) - 2 xy  2 + 15 y  2 - 13 y  3 
C) 8 xy  2 + 13 y  2 - 13 y  3 
D) 2 xy  2 + 13 y  2 - 12 y  3 
E) none of these 
A) - 2 xy  2 + 13 y  2 + 12 y  3 
B) - 2 xy  2 + 15 y  2 - 13 y  3 
C) 8 xy  2 + 13 y  2 - 13 y  3 
D) 2 xy  2 + 13 y  2 - 12 y  3 
E) none of these

Question 17

The number 26,300,000,000,000 is written in __________ notation. And the number $2.63 \times 10 ^ { 13 }$ is written in __________ notation

Accepted Answer

A) standard; scientific 
B) decimal; standard 
C) standard; decimal 
D) scientific; standard 
A) standard; scientific 
B) decimal; standard 
C) standard; decimal 
D) scientific; standard

Question 18

How much money should a young married couple invest now at a(n)6% annual rate if they want to have $100,000 in the bank when they reach retirement age in 40 years? Use the formula: $$P = A ( 1 + i ) ^ { - n }$$ where P is the amount of money to be invested at an annual rate i (expressed as a decimal)in order to have $ A in n years. Round your answer to the nearest integer. $ __________

Accepted Answer

The answer of How much money should a young married...

Question 19

Solve the formula $c = \frac { 1 } { 2 } ( V + t ) y$ for the variable $y$ .

Accepted Answer

A)  $y = \frac { V + t } { 2 c }$ 
B)  $y = \frac { c } { 2 ( V + t ) }$ 
C)  $y = \frac { 2 ( V + t ) } { c }$ 
D)  $y = \frac { 2 c } { V + i }$ 
E)  $y = \frac { c } { 2 V + 2 t }$ 
A)  $y = \frac { V + t } { 2 c }$ 
B)  $y = \frac { c } { 2 ( V + t ) }$ 
C)  $y = \frac { 2 ( V + t ) } { c }$ 
D)  $y = \frac { 2 c } { V + i }$ 
E)  $y = \frac { c } { 2 V + 2 t }$

Question 20

Solve the equation. $( t - 38 ) ^ { 2 }$ = $( t + 38 ) ^ { 2 }$

Accepted Answer

A) 1 
B) 0 
C) 38 
D) -38 
A) 1 
B) 0 
C) 38 
D) -38

Perform the division. $\frac { - 9 a ^ { 2 } b ^ { 2 } - 6 a ^ { 2 } b - 9 a b ^ { 2 } } { - 3 a b }$

Find the product. $\left( 3 t ^ { 6 } z ^ { 6 } \right) \left( 2 t ^ { 2 } z ^ { 2 } \right)$

Simplify the following expression. Assume that $y \neq 0$ . $\frac { 8 y ^ { 4 } \cdot y ^ { 6 } \cdot y ^ { 6 } } { 2 \left( y ^ { 4 } \right) ^ { 3 } }$

Solve the formula $V = 3 ( r - I ) a$ for the variable $r$ .

Write the polynomial with the exponents on x in descending order. $a ^ { 2 } x - a x ^ { 3 } + 2 a ^ { 3 } x ^ { 5 } - 3 a ^ { 3 } x ^ { 2 }$

Subtract. 6-6x+6 3-3x-5

Evaluate $- x ^ { 2 } - 4$ for $x = - 1$ .

Find the quotient. $\frac { 12 x ^ { 7 } y ^ { 9 } } { - 6 x ^ { 5 } y ^ { 4 } }$

Find the indicated product by applying the distributive property and combining similar terms. $\left( x ^ { 2 } - 7 x - 6 \right) \left( x ^ { 2 } + 9 x - 9 \right)$

Perform the division. $\frac { 20 a ^ { 6 } b ^ { 5 } - 12 a ^ { 5 } b ^ { 6 } } { 4 a ^ { 5 } b ^ { 5 } }$

Simplify the following expression. $\left( \frac { 9 } { 16 } \right) ^ { - 1 }$

Find the product. $\left( 2 s ^ { 5 } x ^ { 5 } \right) \left( 3 s ^ { 2 } x ^ { 3 } \right) ( s x )$

Write the number $( 2.15 ) ( 10 ) ^ { 4 }$ in ordinary decimal notation. For example (2.78)(10) ⁴ = 27,800.

Find the product. $( 4 a + t ) ^ { 2 }$

Write the following expression without using a negative exponent. $( - 32 ) ^ { - 1 }$

Simplify the expression. 3 y ( xy + y )- 5 y ²( x - 2 + 3 y )+ 2( y ³+ y ²)

The number 26,300,000,000,000 is written in notation. And the number $2.63 \times 10 ^ { 13 }$ is written in notation

Solve the formula $c = \frac { 1 } { 2 } ( V + t ) y$ for the variable $y$ .

Solve the equation. $( t - 38 ) ^ { 2 }$ = $( t + 38 ) ^ { 2 }$

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Factoring and Quadratic Equations

Rational Expressions and Equations

Roots and Radicals

Quadratic Equations

Filters

Exam 5: Exponents and Polynomials

Perform the division. −9a2b2−6a2b−9ab2−3ab\frac { - 9 a ^ { 2 } b ^ { 2 } - 6 a ^ { 2 } b - 9 a b ^ { 2 } } { - 3 a b }−3ab−9a2b2−6a2b−9ab2​

Find the product. (3t6z6)(2t2z2)\left( 3 t ^ { 6 } z ^ { 6 } \right) \left( 2 t ^ { 2 } z ^ { 2 } \right)(3t6z6)(2t2z2)

Simplify the following expression. Assume that y≠0y \neq 0y=0 . 8y4⋅y6⋅y62(y4)3\frac { 8 y ^ { 4 } \cdot y ^ { 6 } \cdot y ^ { 6 } } { 2 \left( y ^ { 4 } \right) ^ { 3 } }2(y4)38y4⋅y6⋅y6​

Solve the formula V=3(r−I)aV = 3 ( r - I ) aV=3(r−I)a for the variable rrr .

Write the polynomial with the exponents on x in descending order. a2x−ax3+2a3x5−3a3x2a ^ { 2 } x - a x ^ { 3 } + 2 a ^ { 3 } x ^ { 5 } - 3 a ^ { 3 } x ^ { 2 }a2x−ax3+2a3x5−3a3x2

Subtract. 6-6x+6 3-3x-5

Evaluate −x2−4- x ^ { 2 } - 4−x2−4 for x=−1x = - 1x=−1 .

Find the quotient. 12x7y9−6x5y4\frac { 12 x ^ { 7 } y ^ { 9 } } { - 6 x ^ { 5 } y ^ { 4 } }−6x5y412x7y9​

Find the indicated product by applying the distributive property and combining similar terms. (x2−7x−6)(x2+9x−9)\left( x ^ { 2 } - 7 x - 6 \right) \left( x ^ { 2 } + 9 x - 9 \right)(x2−7x−6)(x2+9x−9)

Perform the division. 20a6b5−12a5b64a5b5\frac { 20 a ^ { 6 } b ^ { 5 } - 12 a ^ { 5 } b ^ { 6 } } { 4 a ^ { 5 } b ^ { 5 } }4a5b520a6b5−12a5b6​

Simplify the following expression. (916)−1\left( \frac { 9 } { 16 } \right) ^ { - 1 }(169​)−1

Find the product. (2s5x5)(3s2x3)(sx)\left( 2 s ^ { 5 } x ^ { 5 } \right) \left( 3 s ^ { 2 } x ^ { 3 } \right) ( s x )(2s5x5)(3s2x3)(sx)

Write the number (2.15)(10)4( 2.15 ) ( 10 ) ^ { 4 }(2.15)(10)4 in ordinary decimal notation. For example (2.78)(10) 4 = 27,800.

Find the product. (4a+t)2( 4 a + t ) ^ { 2 }(4a+t)2

Write the following expression without using a negative exponent. (−32)−1( - 32 ) ^ { - 1 }(−32)−1

Simplify the expression. 3 y ( xy + y )- 5 y 2( x - 2 + 3 y )+ 2( y 3 + y 2)

The number 26,300,000,000,000 is written in __________ notation. And the number 2.63×10132.63 \times 10 ^ { 13 }2.63×1013 is written in __________ notation

Solve the formula c=12(V+t)yc = \frac { 1 } { 2 } ( V + t ) yc=21​(V+t)y for the variable yyy .

Solve the equation. (t−38)2( t - 38 ) ^ { 2 }(t−38)2 = (t+38)2( t + 38 ) ^ { 2 }(t+38)2

An Introduction to Algebra

Equations, Inequalities, and Problem Solving

Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Solving Systems of Equations and Inequalities

Factoring and Quadratic Equations

Rational Expressions and Equations

Roots and Radicals

Quadratic Equations

Filters

Perform the division. $\frac { - 9 a ^ { 2 } b ^ { 2 } - 6 a ^ { 2 } b - 9 a b ^ { 2 } } { - 3 a b }$

Find the product. $\left( 3 t ^ { 6 } z ^ { 6 } \right) \left( 2 t ^ { 2 } z ^ { 2 } \right)$

Simplify the following expression. Assume that $y \neq 0$ . $\frac { 8 y ^ { 4 } \cdot y ^ { 6 } \cdot y ^ { 6 } } { 2 \left( y ^ { 4 } \right) ^ { 3 } }$

Solve the formula $V = 3 ( r - I ) a$ for the variable $r$ .

Write the polynomial with the exponents on x in descending order. $a ^ { 2 } x - a x ^ { 3 } + 2 a ^ { 3 } x ^ { 5 } - 3 a ^ { 3 } x ^ { 2 }$

Evaluate $- x ^ { 2 } - 4$ for $x = - 1$ .

Find the quotient. $\frac { 12 x ^ { 7 } y ^ { 9 } } { - 6 x ^ { 5 } y ^ { 4 } }$

Find the indicated product by applying the distributive property and combining similar terms. $\left( x ^ { 2 } - 7 x - 6 \right) \left( x ^ { 2 } + 9 x - 9 \right)$

Perform the division. $\frac { 20 a ^ { 6 } b ^ { 5 } - 12 a ^ { 5 } b ^ { 6 } } { 4 a ^ { 5 } b ^ { 5 } }$

Simplify the following expression. $\left( \frac { 9 } { 16 } \right) ^ { - 1 }$

Find the product. $\left( 2 s ^ { 5 } x ^ { 5 } \right) \left( 3 s ^ { 2 } x ^ { 3 } \right) ( s x )$

Write the number $( 2.15 ) ( 10 ) ^ { 4 }$ in ordinary decimal notation. For example (2.78)(10) ⁴ = 27,800.

Find the product. $( 4 a + t ) ^ { 2 }$

Write the following expression without using a negative exponent. $( - 32 ) ^ { - 1 }$

Simplify the expression. 3 y ( xy + y )- 5 y ²( x - 2 + 3 y )+ 2( y ³+ y ²)

The number 26,300,000,000,000 is written in notation. And the number $2.63 \times 10 ^ { 13 }$ is written in notation

Solve the formula $c = \frac { 1 } { 2 } ( V + t ) y$ for the variable $y$ .

Solve the equation. $( t - 38 ) ^ { 2 }$ = $( t + 38 ) ^ { 2 }$