Question 1

Multiply and simplify.
-$t ^ { 6 } \cdot t ^ { 4 }$

Accepted Answer

A)  $\frac { 1 } { t ^ { 2 } }$ 
B)  $\frac { 1 } { t ^ { 10 } }$ 
C)  $\mathrm { t } ^ { 10 }$ 
D)  $t ^ { 2 }$ 
A)  $\frac { 1 } { t ^ { 2 } }$ 
B)  $\frac { 1 } { t ^ { 10 } }$ 
C)  $\mathrm { t } ^ { 10 }$ 
D)  $t ^ { 2 }$

Question 2

Multiply or divide and write scientific notation for the result.
-$$\frac { 20 \times 10 ^ { 6 } } { 4 \times 10 ^ { 7 } }$$

Accepted Answer

A)  $10 \times 10 ^ { 13 }$ 
B)  $10 \times 10 ^ { - 1 }$ 
C)  $5 \times 10 ^ { - 1 }$ 
D)  $5 \times 10 ^ { 13 }$ 
A)  $10 \times 10 ^ { 13 }$ 
B)  $10 \times 10 ^ { - 1 }$ 
C)  $5 \times 10 ^ { - 1 }$ 
D)  $5 \times 10 ^ { 13 }$

Question 3

Express the following using negative exponents.
-$\frac{1}{t^{12}}$

Accepted Answer

A)  $t ^ { 12 }$ 
B)  $12 ^ { t }$ 
C)  $12 ^ { - t }$ 
D)  $\mathrm { t } ^ { - 12 }$ 
A)  $t ^ { 12 }$ 
B)  $12 ^ { t }$ 
C)  $12 ^ { - t }$ 
D)  $\mathrm { t } ^ { - 12 }$

Question 4

Multiply and simplify.
-$3 ^ { 5 } \cdot 3 ^ { 3 }$

Accepted Answer

A)  1 
B)  $3 ^ { 8 }$ 
C)  311 
D)  8 
A)  1 
B)  $3 ^ { 8 }$ 
C)  311 
D)  8

Question 5

Evaluate the polynomial.
-$4 x ^ { 3 } + 5 x ^ { 2 } - 15$, when $x = - 2$

Accepted Answer

A)  $- 37$ 
B)  $- 39$ 
C)  $- 57$ 
D)  $- 27$ 
A)  $- 37$ 
B)  $- 39$ 
C)  $- 57$ 
D)  $- 27$

Question 6

Identify the coefficient of each term of the polynomial.
-$2 a + 5 a ^ { 2 }$

Accepted Answer

A)  2 and 5 
B)  2 
C)  $- 2$ and 5 
D)  $- 2$ 
A)  2 and 5 
B)  2 
C)  $- 2$ and 5 
D)  $- 2$

Question 7

Express the following using negative exponents.
-$\frac { 1 } { b ^ { 2 } }$

Accepted Answer

A)  $b ^ { - 2 }$ 
B)  $2 ^ { - \mathrm { b } }$ 
C)  $2 ^ { - \mathrm { b } - 1 }$ 
D)  $b ^ { 2 }$ 
A)  $b ^ { - 2 }$ 
B)  $2 ^ { - \mathrm { b } }$ 
C)  $2 ^ { - \mathrm { b } - 1 }$ 
D)  $b ^ { 2 }$

Question 8

Multiply and simplify.
-$x \cdot x^{-5}$

Accepted Answer

A)  $\frac { 1 } { x ^ { 4 } }$ 
B)  $\frac { 1 } { x ^ { 6 } }$ 
C)  $x ^ { 4 }$ 
D)  $x ^ { 6 }$ 
A)  $\frac { 1 } { x ^ { 4 } }$ 
B)  $\frac { 1 } { x ^ { 6 } }$ 
C)  $x ^ { 4 }$ 
D)  $x ^ { 6 }$

Question 9

Multiply and simplify.
-$\left( x ^ { 2 } y ^ { 5 } \right) \left( x ^ { 7 } y \right)$

Accepted Answer

A)  $x ^ { 14 } y ^ { 5 }$ 
B)  $x ^ { 9 } y ^ { 5 }$ 
C)  $x ^ { 9 } y ^ { 6 }$ 
D)  $2 x ^ { 9 } 2 y ^ { 6 }$ 
A)  $x ^ { 14 } y ^ { 5 }$ 
B)  $x ^ { 9 } y ^ { 5 }$ 
C)  $x ^ { 9 } y ^ { 6 }$ 
D)  $2 x ^ { 9 } 2 y ^ { 6 }$

Question 10

Multiply or divide and write scientific notation for the result.
-$\frac { 21.62 \times 10 ^ { 3 } } { 4.6 \times 10 ^ { - 1 } }$

Accepted Answer

A)  $9.4 \times 10 ^ { 4 }$ 
B)  $4.7 \times 10 ^ { 2 }$ 
C)  $4.7 \times 10 ^ { 4 }$ 
D)  $9.4 \times 10 ^ { 2 }$ 
A)  $9.4 \times 10 ^ { 4 }$ 
B)  $4.7 \times 10 ^ { 2 }$ 
C)  $4.7 \times 10 ^ { 4 }$ 
D)  $9.4 \times 10 ^ { 2 }$

Question 11

Evaluate.
-$$6 ^ { 1 }$$

Accepted Answer

A) 1 
B) 0 
C) 6 
D) 36 
A) 1 
B) 0 
C) 6 
D) 36

Question 12

Multiply and simplify.
-$$x ^ { - 9 } \cdot x ^ { 3 } \cdot x ^ { - 8 }$$

Accepted Answer

A)  $x ^ { 20 }$ 
B)  $\times ^ { 14 }$ 
C)  $\frac { 1 } { x ^ { 20 } }$ 
D)  $\frac { 1 } { \mathrm { x } ^ { 14 } }$ 
A)  $x ^ { 20 }$ 
B)  $\times ^ { 14 }$ 
C)  $\frac { 1 } { x ^ { 20 } }$ 
D)  $\frac { 1 } { \mathrm { x } ^ { 14 } }$

Question 13

Express using positive exponents. Then simplify.
-$\left( \frac { 2 } { 5 } \right) ^ { - 2 }$

Accepted Answer

A)  $\frac { 4 } { 25 }$ 
B)  $\frac { 25 } { 4 }$ 
C)  $- \frac { 25 } { 4 }$ 
D)  $- \frac { 4 } { 25 }$ 
A)  $\frac { 4 } { 25 }$ 
B)  $\frac { 25 } { 4 }$ 
C)  $- \frac { 25 } { 4 }$ 
D)  $- \frac { 4 } { 25 }$

Question 14

What is the meaning of the expression?
-$$( - 8.7 ) ^ { 3 }$$

Accepted Answer

A) -8.7 ·8.7 ·8.7 
B) 3(-8.7) 
C) (-8.7)(-8.7)(-8.7) 
D) (8.7)(8.7)(8.7) 
A) -8.7 ·8.7 ·8.7 
B) 3(-8.7) 
C) (-8.7)(-8.7)(-8.7) 
D) (8.7)(8.7)(8.7)

Question 15

Write the number in scientific notation.
-0.000007064

Accepted Answer

A)  $7.064 \times 10 ^ { - 5 }$ 
B)  $7.064 \times 10 ^ { - 7 }$ 
C)  $7.064 \times 10 ^ { - 6 }$ 
D)  $7.064 \times 10 ^ { 6 }$ 
A)  $7.064 \times 10 ^ { - 5 }$ 
B)  $7.064 \times 10 ^ { - 7 }$ 
C)  $7.064 \times 10 ^ { - 6 }$ 
D)  $7.064 \times 10 ^ { 6 }$

Question 16

Evaluate the polynomial.
-$2 x ^ { 3 } - 6 x ^ { 2 } + 18$, when $x = 4$

Accepted Answer

A)  40 
B)  50 
C)  38 
D)  122 
A)  40 
B)  50 
C)  38 
D)  122

Question 17

What is the meaning of the expression?
-$- 3 q ^ { 3 }$

Accepted Answer

A)  $( - 3 q ) ( - 3 q ) ( - 3 q )$ 
B)  $- 3 \cdot q \cdot 3$ 
C)  $- 3 \cdot q \cdot q \cdot q$ 
D)  $( - 3 ) ( - 3 ) ( - 3 ) ( q )$ 
A)  $( - 3 q ) ( - 3 q ) ( - 3 q )$ 
B)  $- 3 \cdot q \cdot 3$ 
C)  $- 3 \cdot q \cdot q \cdot q$ 
D)  $( - 3 ) ( - 3 ) ( - 3 ) ( q )$

Question 18

Divide and simplify.
-$\frac { z ^ { - 9 } } { z ^ { - 5 } }$

Accepted Answer

A)  $\mathrm { z } ^ { 14 }$ 
B)  $\frac { 1 } { z ^ { - 4 } }$ 
C)  $\frac { 1 } { z ^ { 4 } }$ 
D)  $\mathrm { z } ^ { 4 }$ 
A)  $\mathrm { z } ^ { 14 }$ 
B)  $\frac { 1 } { z ^ { - 4 } }$ 
C)  $\frac { 1 } { z ^ { 4 } }$ 
D)  $\mathrm { z } ^ { 4 }$

Question 19

Multiply and simplify.
-$$\left( m n ^ { 6 } \right) \left( m ^ { 3 } n ^ { 6 } \right)$$

Accepted Answer

A)  $2 m ^ { 4 } 2 n ^ { 12 }$ 
B)  $m ^ { 4 } n ^ { 12 }$ 
C)  $\mathrm { m } ^ { 3 } \mathrm { n } ^ { 12 }$ 
D)  $m ^ { 3 } n ^ { 36 }$ 
A)  $2 m ^ { 4 } 2 n ^ { 12 }$ 
B)  $m ^ { 4 } n ^ { 12 }$ 
C)  $\mathrm { m } ^ { 3 } \mathrm { n } ^ { 12 }$ 
D)  $m ^ { 3 } n ^ { 36 }$

Question 20

What is the meaning of the expression?
-$$4^6$$

Accepted Answer

A) 46 
B) 4 ·4 ·4 ·4 ·4 ·4 
C) 5 
D) 6 ·4 
A) 46 
B) 4 ·4 ·4 ·4 ·4 ·4 
C) 5 
D) 6 ·4

Multiply and simplify. - $t ^ { 6 } \cdot t ^ { 4 }$

Multiply or divide and write scientific notation for the result. - $\frac { 20 \times 10 ^ { 6 } } { 4 \times 10 ^ { 7 } }$

Express the following using negative exponents. - $\frac{1}{t^{12}}$

Multiply and simplify. - $3 ^ { 5 } \cdot 3 ^ { 3 }$

Evaluate the polynomial. - $4 x ^ { 3 } + 5 x ^ { 2 } - 15$ , when $x = - 2$

Identify the coefficient of each term of the polynomial. - $2 a + 5 a ^ { 2 }$

Express the following using negative exponents. - $\frac { 1 } { b ^ { 2 } }$

Multiply and simplify. - $x \cdot x^{-5}$

Multiply and simplify. - $\left( x ^ { 2 } y ^ { 5 } \right) \left( x ^ { 7 } y \right)$

Multiply or divide and write scientific notation for the result. - $\frac { 21.62 \times 10 ^ { 3 } } { 4.6 \times 10 ^ { - 1 } }$

Evaluate. - $6 ^ { 1 }$

Multiply and simplify. - $x ^ { - 9 } \cdot x ^ { 3 } \cdot x ^ { - 8 }$

Express using positive exponents. Then simplify. - $\left( \frac { 2 } { 5 } \right) ^ { - 2 }$

What is the meaning of the expression? - $( - 8.7 ) ^ { 3 }$

Write the number in scientific notation. -0.000007064

Evaluate the polynomial. - $2 x ^ { 3 } - 6 x ^ { 2 } + 18$ , when $x = 4$

What is the meaning of the expression? - $- 3 q ^ { 3 }$

Divide and simplify. - $\frac { z ^ { - 9 } } { z ^ { - 5 } }$

Multiply and simplify. - $\left( m n ^ { 6 } \right) \left( m ^ { 3 } n ^ { 6 } \right)$

What is the meaning of the expression? - $4^6$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Factoring

Rational Expressions and Equations

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Filters

Exam 4: Polynomials: Operations

Multiply and simplify. - t6⋅t4t ^ { 6 } \cdot t ^ { 4 }t6⋅t4

Multiply or divide and write scientific notation for the result. - 20×1064×107\frac { 20 \times 10 ^ { 6 } } { 4 \times 10 ^ { 7 } }4×10720×106​

Express the following using negative exponents. - 1t12\frac{1}{t^{12}}t121​

Multiply and simplify. - 35⋅333 ^ { 5 } \cdot 3 ^ { 3 }35⋅33

Evaluate the polynomial. - 4x3+5x2−154 x ^ { 3 } + 5 x ^ { 2 } - 154x3+5x2−15 , when x=−2x = - 2x=−2

Identify the coefficient of each term of the polynomial. - 2a+5a22 a + 5 a ^ { 2 }2a+5a2

Express the following using negative exponents. - 1b2\frac { 1 } { b ^ { 2 } }b21​

Multiply and simplify. - x⋅x−5x \cdot x^{-5}x⋅x−5

Multiply and simplify. - (x2y5)(x7y)\left( x ^ { 2 } y ^ { 5 } \right) \left( x ^ { 7 } y \right)(x2y5)(x7y)

Multiply or divide and write scientific notation for the result. - 21.62×1034.6×10−1\frac { 21.62 \times 10 ^ { 3 } } { 4.6 \times 10 ^ { - 1 } }4.6×10−121.62×103​

Evaluate. - 616 ^ { 1 }61

Multiply and simplify. - x−9⋅x3⋅x−8x ^ { - 9 } \cdot x ^ { 3 } \cdot x ^ { - 8 }x−9⋅x3⋅x−8

Express using positive exponents. Then simplify. - (25)−2\left( \frac { 2 } { 5 } \right) ^ { - 2 }(52​)−2

What is the meaning of the expression? - (−8.7)3( - 8.7 ) ^ { 3 }(−8.7)3