0. Review of Algebra

Exponents

0. Review of Algebra

Exponents

Guided videos.

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Guided course

7:39

Introduction to Exponent Rules

Zero and Negative Rules

Simplifying Exponential Expressions

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05:27

Power of a Product Property

Power of a Product Property

Power of a Quotient Property

Power of a Quotient Property

Power of a Quotient Property

Simplifying expressions using the Laws of Exponents

Algebra - Simplify an expression with exponents

Exponents and integers

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Showing 8 of 8 videos

Practice this topic

Multiple Choice

Simplify the expression using exponent rules.

$(- 5 a^{2}) (3 a^{2})$

Simplify the expression using exponent rules.

$-\frac{12b^{11}}{4b^7}$

Rewrite the expression using exponent rules.

$\left(4x^2\right)^3$

Rewrite the expression using exponent rules.

$\left(\frac{3x^4}{y^{-2}}\right)^3$

In Exercises 1–14, write each number in decimal notation without the use of exponents. 3.8X10²

In Exercises 1–6, find the intersection of the sets. { 1, 2, 3, 4} ⋂ {2, 4, 5}

In Exercises 1–12, find each absolute value. |-7|

In the fraction 5/8, 5 is the numerator and 8 is the denominator.

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Textbook Question

The mixed number equivalent of the improper fraction 31/5 is 6(1/5).

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Textbook Question

In Exercises 1–12, find each absolute value. |4|

The reciprocal of 6/2 is 3/1.

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Textbook Question

Let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set A ∩ B.

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Textbook Question

In Exercises 1–6, find the intersection of the sets. { a, b, c, d} ⋂ ∅

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Textbook Question

Fill in the blank(s) to correctly complete each sentence. In the expression 6^3, 6 is the ____ , and 3 is the ____ .

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Textbook Question

Identify the set { 1,1/3, 1/9 ,1/27, ....} as finite or infinite.

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Textbook Question

Let A = {a, b, c}, B = {a, c, d, e}, and C = {a, d, f, g}. Find the indicated set A ∪ B.

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Textbook Question

In Exercises 1–12, find each absolute value. |-7.6|

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Textbook Question

In Exercises 1–14, write each number in decimal notation without the use of exponents. -7.16X10⁶

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Textbook Question

Which choice shows the correct way to write 16/24 in lowest terms? A. 16/24 = (8 + 8)/(8 + 16) =8/16 =1/2 B.16/24 =(4*4)/(4 *6) =4/6 C. 16/24 =(8*2)/(8*3) =2/3

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Textbook Question

Evaluate each expression. 0/7

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Textbook Question

Use set notation and write the elements belonging to the set {x | x is a natural number less than 6}.

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Textbook Question

Which fraction is not equal to 5/9? A. 15/27 B. 30/54 C. 40/74 D. 55/99

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Textbook Question

Evaluate each expression. 10^3

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Textbook Question

In Exercises 1–14, write each number in decimal notation without the use of exponents. 1.4X10⁰

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Textbook Question

Write each fraction in lowest terms. 8/16

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Textbook Question

Let U = {1, 2, 3, 4, 5} and A = {1, 2, 3}. Find A′.

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Textbook Question

Evaluate each expression. 2*5 - 10/12

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Textbook Question

Write each fraction in lowest terms. 4/12

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Textbook Question

Find {16, 18, 21, 50} ∩ {15, 16, 17, 18}.

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Textbook Question

In Exercises 1–14, write each number in decimal notation without the use of exponents. 7.9X10⁻¹

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Textbook Question

Evaluate each expression. |-4|

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Textbook Question

Find {16, 18, 21, 50} ∪ {15, 16, 17, 18}.

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Textbook Question

In Exercises 1–12, find each absolute value. |-√2|

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Textbook Question

Write each fraction in lowest terms. 16/20

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Textbook Question

Write each fraction in lowest terms. 90/150

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Textbook Question

Identify each set as finite or infinite. Then determine whether 10 is an element of the set. {4, 5, 6,...., 15}

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Textbook Question

Evaluate each expression. |-10|

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Textbook Question

In Exercises 1–12, find each absolute value. -|-2/5|

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Textbook Question

Write each fraction in lowest terms. 100/140

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Textbook Question

Evaluate each expression. |-15|

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Textbook Question

Write each fraction in lowest terms. 18/90

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Textbook Question

Identify each set as finite or infinite. Then determine whether 10 is an element of the set. {1, 1/2, 1/4, 1/8, ....}

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Textbook Question

Evaluate each expression. -|4/7|

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Textbook Question

State the name of the property illustrated: 3+17 = 17+3

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Textbook Question

In Exercises 1–14, write each number in decimal notation without the use of exponents. -6.00001X10¹⁰

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Textbook Question

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √27

Write each fraction in lowest terms. 16/64

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Textbook Question

Evaluate each expression. -|7/2|

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Textbook Question

State the name of the property illustrated: (6 • 3) • 9 = 6 • (3 • 9)

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Textbook Question

Identify each set as finite or infinite. Then determine whether 10 is an element of the set. {x | x is a natural number greater than 11}

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Textbook Question

Evaluate each expression. -|-3|

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Textbook Question

In Exercises 15–30, write each number in scientific notation. 32,000

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Textbook Question

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √125x^2

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Textbook Question

Evaluate each expression. -|-12|

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Textbook Question

Determine whether each statement is true or false. |25| = |-25|

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Textbook Question

In Exercises 15–30, write each number in scientific notation. 638,000,000,000,000,000

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Textbook Question

Identify each set as finite or infinite. Then determine whether 10 is an element of the set. {x | x is a fraction between 8 and 9}

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Textbook Question

The formula C=5/9(F-32) expresses the relationship between Fahrenheit temperature, F, and Celsius temperature, C. In Exercises 17–18, use the formula to convert the given Fahrenheit temperature to its equivalent temperature on the Celsius scale. 50 °F

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Textbook Question

Write each improper fraction as a mixed number. 17/12

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Textbook Question

Write each improper fraction as a mixed number. 16/9

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Textbook Question

State the name of the property illustrated: (3 • 7) + (4 • 7) = (4 • 7) + (3 •7)

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Textbook Question

Determine whether each statement is true or false. |5+(-13) | = |5| + |-13|

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Textbook Question

A football was kicked vertically upward from a height of 4 feet with an initial speed of 60 feet per second. The formula h=4+60t-16t^2 describes the ball's height above the ground, h, in feet, t seconds after it was kicked. Use this formula to solve Exercises 19–20. What was the ball's height 2 seconds after it was kicked?

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Textbook Question

In Exercises 15–30, write each number in scientific notation. -317

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Textbook Question

Use set notation, and list all the elements of each set. {12, 13, 14,..., 20}

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Textbook Question

Write each improper fraction as a mixed number. 77/12

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Textbook Question

Determine whether each statement is true or false. |8-12| = |8| - |12|

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Textbook Question

In Exercises 21–28, find the intersection of the sets. {1,2,3,4}∩{2,4,5}

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Textbook Question

In Exercises 15–30, write each number in scientific notation. -5716

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Textbook Question

Use set notation, and list all the elements of each set. {1, 1/2, 1/4, ...., 1/32} .

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Textbook Question

Write each mixed number as an improper fraction. 2(3/5)

Determine whether each statement is true or false. |11| * |-6| = |-66|

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Textbook Question

Determine whether each statement is true or false. |-5| * |6| = |-5*6|

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Textbook Question

Use set notation, and list all the elements of each set. {17, 22, 27, .. , 47}

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Textbook Question

In Exercises 15–30, write each number in scientific notation. 0.0027

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Textbook Question

In Exercises 21–28, find the intersection of the sets. {s,e,t}∩{t,e,s}

Determine whether each statement is true or false. |-14| / |2| = |-14/2|

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Textbook Question

Use set notation, and list all the elements of each set. {74, 68, 62, ..., 38}

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Textbook Question

Evaluate each exponential expression: (-3)^3 (-2)^2

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Textbook Question

Use set notation, and list all the elements of each set. {x | x is a natural number greater than 8 and less than 15}

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Textbook Question

In Exercises 15–30, write each number in scientific notation. -0.00000000504

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Textbook Question

Multiply or divide as indicated. Write answers in lowest terms as needed. (4/5)*(6/7)

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Textbook Question

Evaluate each exponential expression: 2^(-4) + 4^(-1)

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Textbook Question

Use set notation, and list all the elements of each set. {x | x is a natural number not greater than 4}

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Textbook Question

Evaluate each exponential expression: 5^(-3) • 5

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Textbook Question

Multiply or divide as indicated. Write answers in lowest terms as needed. (5/9)*(2/7)

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Textbook Question

Evaluate each exponential expression: (3^3)/(3^6)

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Textbook Question

Insert ∈ or ∉ in each blank to make the resulting statement true. 6 _____ {3, 4, 5, 6}

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Textbook Question

In Exercises 15–30, write each number in scientific notation. 0.007

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Textbook Question

In Exercises 21–28, find the intersection of the sets. {a,b,c,d}∩∅

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Textbook Question

Find each sum or difference. -6 + (-13)

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Textbook Question

Multiply or divide as indicated. Write answers in lowest terms as needed. (3/20)*(5/21)

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Textbook Question

Simplify each exponential expression: (-2x^4y^3)^3

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Textbook Question

Insert ∈ or ∉ in each blank to make the resulting statement true. 5 ____ {4, 6, 8, 10}

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Textbook Question

In Exercises 15–30, write each number in scientific notation. 3.14159

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Textbook Question

Find each sum or difference. -15+6

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Textbook Question

Simplify each exponential expression: (-5x^3y^2)(-2x^(-11)y^(-2))

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Textbook Question

Multiply or divide as indicated. Write answers in lowest terms as needed. (1/8)*(10/7)

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Textbook Question

Insert ∈ or ∉ in each blank to make the resulting statement true. 13 _____ {3, 5, 12, 14}

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Textbook Question

In Exercises 29–34, find the union of the sets. {1,3,5,7}∪{2,4,6,8,10}

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