Exponents and Order of Operations
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Questions and Answers

(______)⁵ = 2/3 × 2/3 × 2/3 × 2/3 × 2/3 × 2/3 × 2/3 × 2/3 × 2/3 × 2/3

-7

(-5)³ = ?

-125

3³ = ?

27

(1 1/3)² = ?

<p>16/9</p> Signup and view all the answers

(53 - (-10)) ÷ (-3)² = ?

<p>14</p> Signup and view all the answers

-6 - 1 × 3 1/3 = ?

<p>-9 1/3</p> Signup and view all the answers

(-1/2 ÷ (-1/3)) + (1/3 ÷ (-3/4)) = ?

<p>-1/6</p> Signup and view all the answers

(-1/4)² + 18 x (2 - 5)² = ?

<p>230 1/16</p> Signup and view all the answers

Flashcards

Exponential Form

A base multiplied by itself a number of times, indicated by the exponent.

Expanded Form

The expanded form shows the base multiplied by itself the number of times indicated by the exponent.

Standard Form

The value of a number raised to a power.

Exponent

A number that indicates how many times a base is multiplied by itself.

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Base

The number being multiplied by itself in an exponential expression.

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Power

A number multiplied by itself a specific number of times.

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Order of Operations

A mathematical rule that defines the order in which operations should be performed.

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Evaluating Expressions

The process of solving mathematical expressions.

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Negative Number

A numerical value that is less than zero.

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Multiplication

A mathematical operation that indicates repeated addition.

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Addition

A mathematical operation that combines numbers to find their total.

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Subtraction

A mathematical operation that finds the difference between two numbers.

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Division

A mathematical operation that divides a number into equal parts.

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PEMDAS

A set of rules that determines the order in which operations are performed in a mathematical expression.

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Order of Operations: Left-to-Right

Operations that have the same priority in PEMDAS are performed from left to right.

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Variable

A symbolic representation of a number used in mathematical expressions.

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Algebraic Expression

A mathematical expression that contains variables, constants, and operations.

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Equation

A mathematical statement that shows the equality of two expressions.

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Inequality

A mathematical statement that shows the inequality of two expressions.

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Constant

A number that remains constant and does not change.

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Rational Number

A number that can be expressed as a fraction p/q, where p and q are integers and q is not equal to zero.

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Irrational Number

A number that cannot be expressed as a fraction.

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Sequence

A group of numbers arranged in a specific order.

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Common Difference

The difference between consecutive terms in a sequence.

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Arithmetic Sequence

A sequence where the difference between consecutive terms is constant.

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Rate

A ratio of two quantities.

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Central Tendency

A value that represents the center of a set of data.

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Measure of Variability

A value that represents the spread or variability of a set of data.

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Mean

The average of a set of numbers.

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Median

The middle value in a set of ordered numbers.

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Mode

The value that appears most frequently in a set of numbers.

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Graph

A diagram used to represent data graphically.

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Study Notes

Exponents and Order of Operations

  • Exponential Form to Expanded Form: Convert exponential expressions into their expanded form. For example, (-7)5 expands to (-7) x (-7) x (-7) x (-7) x (-7).
  • Finding the Value of Exponential Expressions: Evaluate expressions like (-5)3 to determine their numerical value.
  • Order of Operations (PEMDAS/BODMAS): Solve problems involving multiple operations. This includes parentheses/brackets, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
  • Number Lines for Addition and Subtraction: Use number lines to visualize addition and subtraction problems.

Mixed Numbers

  • Answers should be in lowest terms when dealing with mixed numbers.

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Description

This quiz covers key concepts in exponents and the order of operations, including converting exponential expressions to expanded form and evaluating them. Additionally, you'll practice using the PEMDAS/BODMAS rules to solve multi-step problems and visualize addition and subtraction using number lines. Mixed numbers will also be addressed, ensuring answers are in their lowest terms.

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