Math Gr 8 Ch 4 SUM: Exponents
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Questions and Answers

What is the result of adding an integer to its additive inverse?

  • The result is always positive
  • The result is always negative
  • The result is 0 (correct)
  • The result is undefined

    • Which property states that the order of multiplication does not change the product?

  • Associative Property
  • Distributive Property
  • Commutative Property (correct)
  • Additive Inverse Property

    • What is the effect of subtracting an integer?

  • It has the same effect as adding its additive inverse (correct)
  • It has the same effect as adding the integer
  • It has the same effect as multiplying the integer
  • It has no effect

    • What is the result of multiplying a positive integer and a negative integer?

    <p>The result is always negative</p> Signup and view all the answers

    What is a closed number sentence?

    <p>An equation where all numbers are known</p> Signup and view all the answers

    What is the Distributive Property of Multiplication?

    <p>Multiplication distributes over addition and subtraction</p> Signup and view all the answers

    What is the result of adding an integer and its additive inverse?

    <p>The result is 0</p> Signup and view all the answers

    What is the property that states that integers can be added and subtracted in any order?

    <p>Associative Property of Addition</p> Signup and view all the answers

    What is the result of raising a number to the power of zero?

    <p>The number becomes one</p> Signup and view all the answers

    What is the product of two negative integers?

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

    What is the result of squaring a fraction?

    <p>A new fraction where both the numerator and denominator are squared</p> Signup and view all the answers

    What is the purpose of the order of operations (PEMDAS/BODMAS)?

    <p>To simplify expressions</p> Signup and view all the answers

    What is the result of dividing a positive integer by a negative integer?

    <p>A negative integer</p> Signup and view all the answers

    What is the law of exponents that states that $a^m imes a^n = a^{m+n}$?

    <p>Product of Powers</p> Signup and view all the answers

    What is the result of cubing a fraction?

    <p>A new fraction where both the numerator and denominator are cubed</p> Signup and view all the answers

    What is the purpose of scientific notation?

    <p>To express large numbers in a more readable form</p> Signup and view all the answers

    What is the result of adding a negative integer to another negative integer?

    <p>A larger negative integer</p> Signup and view all the answers

    What is the Distributive Property of multiplication?

    <p>Multiplication distributes over addition and subtraction</p> Signup and view all the answers

    What is the result of adding an integer and its additive inverse?

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

    Which property of integers allows you to add and subtract them in any order?

    <p>Both A and B</p> Signup and view all the answers

    What is the effect of subtracting a negative integer?

    <p>It increases the value</p> Signup and view all the answers

    What type of equation has some unknown numbers?

    <p>Open number sentence</p> Signup and view all the answers

    Which symbol is used to indicate that one integer is greater than another?

    <p>&gt;</p> Signup and view all the answers

    What is the purpose of the temperature rise problem?

    <p>To calculate the difference between two temperatures</p> Signup and view all the answers

    What happens when you subtract a negative integer?

    <p>The value increases</p> Signup and view all the answers

    Which of the following is an example of an open number sentence?

    <p>x + 2 = 7</p> Signup and view all the answers

    What is the purpose of finding the difference in depths between two trenches?

    <p>To compare the depths of the two trenches</p> Signup and view all the answers

    What is the effect of adding an integer to its additive inverse?

    <p>The result is always zero</p> Signup and view all the answers

    What symbol is used to indicate that one integer is less than another?

    <p>&lt;</p> Signup and view all the answers

    What is the purpose of finding the maximum temperature from the minimum temperature and the rise?

    <p>To compare the temperatures</p> Signup and view all the answers

    Which of the following statements about integers is true?

    <p>The product of two positive integers is always positive.</p> Signup and view all the answers

    What is the purpose of additive inverses in integer operations?

    <p>To find the sum of an integer and its negative counterpart.</p> Signup and view all the answers

    Which property of integers allows you to rewrite the expression (a + b) + c as a + (b + c)?

    <p>Associative Property of Addition</p> Signup and view all the answers

    What is the effect of adding a negative integer to another integer?

    <p>It decreases the value of the integer.</p> Signup and view all the answers

    Which symbol is used to indicate that one integer is less than or equal to another?

    <p>&lt;</p> Signup and view all the answers

    What is the result of multiplying a negative integer by a negative integer?

    <p>A positive integer</p> Signup and view all the answers

    Which of the following is an example of an open number sentence?

    <p>x + 2 = 5</p> Signup and view all the answers

    What is the result of adding an integer and its additive inverse?

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

    What is the result of raising 2 to the power of 3?

    <p>8</p> Signup and view all the answers

    What is the simplified form of the expression (3^2) × (3^4)?

    <p>3^6</p> Signup and view all the answers

    What is the result of dividing 4^3 by 4^2?

    <p>4^1</p> Signup and view all the answers

    What is the result of multiplying (2^3) by (3^2)?

    <p>6^3</p> Signup and view all the answers

    What is the result of converting 3000 to scientific notation?

    <p>3 × 10^3</p> Signup and view all the answers

    What is the result of subtracting 2^3 from 3^3?

    <p>5</p> Signup and view all the answers

    What is the result of multiplying (-2)^3 by (-2)^2?

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

    What is the result of adding 2^3 to 3^2?

    <p>15</p> Signup and view all the answers

    What is the result of dividing (-3)^4 by (-3)^2?

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

    What is the result of cubing the fraction 2/3?

    <p>8/27</p> Signup and view all the answers

    What is the result of subtracting 5 from -3?

    <p>-8</p> Signup and view all the answers

    Which of the following statements about integers is true?

    <p>Integers can be added and subtracted in any order due to the commutative and associative properties.</p> Signup and view all the answers

    What is the additive inverse of 5?

    <p>-5</p> Signup and view all the answers

    What is the result of adding 3 and -5?

    <p>-2</p> Signup and view all the answers

    Which symbol is used to indicate that one integer is greater than or equal to another?

    <p>&gt;=</p> Signup and view all the answers

    What is the result of subtracting -3 from 2?

    <p>5</p> Signup and view all the answers

    Which of the following statements about integers is true?

    <p>The product of a positive and a negative integer is always negative.</p> Signup and view all the answers

    What is the purpose of additive inverses in integer operations?

    <p>To find the sum of an integer and its negative counterpart.</p> Signup and view all the answers

    Which property of integers allows you to rewrite the expression (a + b) + c as a + (b + c)?

    <p>Associative Property of Addition</p> Signup and view all the answers

    What is the effect of adding an integer to its additive inverse?

    <p>The result is always zero.</p> Signup and view all the answers

    Which symbol is used to indicate that one integer is greater than another?

    <p>&gt;</p> Signup and view all the answers

    What is the purpose of the Distributive Property of Multiplication?

    <p>To multiply integers over addition and subtraction.</p> Signup and view all the answers

    Which of the following is NOT a property of integer addition?

    <p>Distributive Property</p> Signup and view all the answers

    What happens when you subtract an integer from its additive inverse?

    <p>The result is always the original integer.</p> Signup and view all the answers

    What is the result of multiplying $a^m$ and $a^n$?

    <p>$a^{m+n}$</p> Signup and view all the answers

    What is the result of dividing $a^m$ by $a^n$?

    <p>$a^{m-n}$</p> Signup and view all the answers

    What is the result of raising $a^m$ to the power of $n$?

    <p>$a^{m imes n}$</p> Signup and view all the answers

    What is the result of converting 4500 to scientific notation?

    <p>4.5 × 10^3</p> Signup and view all the answers

    What is the result of comparing two numbers in scientific notation?

    <p>Compare the exponents first</p> Signup and view all the answers

    What is the result of adding a positive integer and a negative integer?

    <p>The result depends on the values of the integers</p> Signup and view all the answers

    What is the result of subtracting a negative integer from another integer?

    <p>The result is always positive</p> Signup and view all the answers

    What is the result of multiplying two integers with the same sign?

    <p>The result is always positive</p> Signup and view all the answers

    What is the result of dividing a positive integer by a negative integer?

    <p>The result is always negative</p> Signup and view all the answers

    What is the result of squaring a fraction?

    <p>The result is a new fraction with both the numerator and the denominator squared</p> Signup and view all the answers

    What is the outcome of adding a negative integer to its additive inverse?

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

    What is the effect of subtracting a positive integer from a negative integer?

    <p>The result will be a negative integer</p> Signup and view all the answers

    Which of the following is an example of an open number sentence involving integers?

    <p>x + 2 = 5</p> Signup and view all the answers

    What is the purpose of using the commutative property of addition when working with integers?

    <p>To change the order of addition</p> Signup and view all the answers

    What is the outcome of subtracting a negative integer from another negative integer?

    <p>A positive integer</p> Signup and view all the answers

    Which of the following is a real-world application of integer operations?

    <p>Finding the difference in height between a mountain and the surrounding ocean</p> Signup and view all the answers

    What is the result of multiplying $a^m$ by $a^n$ where $m$ and $n$ are integers?

    <p>$a^{m+n}$</p> Signup and view all the answers

    What is the result of raising a negative integer to an even power?

    <p>Always positive</p> Signup and view all the answers

    What is the result of dividing $a^m$ by $a^n$ where $m$ and $n$ are integers?

    <p>$a^{m-n}$</p> Signup and view all the answers

    What is the result of multiplying a negative integer by a negative integer?

    <p>Always positive</p> Signup and view all the answers

    What is the result of adding a positive integer to a negative integer?

    <p>Depends on the integers</p> Signup and view all the answers

    What is the result of squaring a negative fraction?

    <p>Always positive</p> Signup and view all the answers

    What is the result of converting 0.0003 to scientific notation?

    <p>3 × 10^(-4)</p> Signup and view all the answers

    What is the result of multiplying two integers with different signs?

    <p>Always negative</p> Signup and view all the answers

    What is the result of subtracting a negative integer from a positive integer?

    <p>Always positive</p> Signup and view all the answers

    What is the result of cubing a negative fraction?

    <p>Always negative</p> Signup and view all the answers

    What is the primary purpose of additive inverses in integer operations?

    <p>To represent the same value but with opposite signs</p> Signup and view all the answers

    Which property of integers allows you to rewrite the expression a + (b + c) as (a + b) + c?

    <p>Associative Property of Addition</p> Signup and view all the answers

    What is the result of multiplying a negative integer by a negative integer?

    <p>A positive integer</p> Signup and view all the answers

    Which symbol is used to indicate that one integer is greater than or equal to another?

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

    What is the primary purpose of the Distributive Property of Multiplication?

    <p>To expand a product of a sum into a sum of products</p> Signup and view all the answers

    What is the result of subtracting an integer from its additive inverse?

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

    Which property of integers allows you to add and subtract them in any order?

    <p>Associative Property of Addition</p> Signup and view all the answers

    What is the result of adding a negative integer to its additive inverse?

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

    What is the result of adding a negative integer to its additive inverse?

    <p>0</p> Signup and view all the answers

    Which property of integers allows you to rewrite the expression a + (b + c) as (a + b) + c?

    <p>Associative Property of Addition</p> Signup and view all the answers

    What is the effect of subtracting a positive integer from another positive integer?

    <p>The result can be either positive or negative</p> Signup and view all the answers

    Which symbol is used to indicate that one integer is less than or equal to another?

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

    What is the result of multiplying a positive integer by a negative integer?

    <p>Always a negative integer</p> Signup and view all the answers

    Which property of integers allows you to add integers in any order?

    <p>Commutative Property of Addition</p> Signup and view all the answers

    What is the result of adding an integer to its additive inverse?

    <p>0</p> Signup and view all the answers

    Which property of integers allows you to rewrite the expression a × (b + c) as (a × b) + (a × c)?

    <p>Distributive Property of Multiplication</p> Signup and view all the answers

    What is the correct order of operations when evaluating an expression with multiple integers and operations?

    <p>From outside in, based on the order of operations (PEMDAS/BODMAS)</p> Signup and view all the answers

    If Sara has a temperature of -5°C and it rises by 8°C, what is her new temperature?

    <p>3°C</p> Signup and view all the answers

    What is the result of subtracting 3 from -2?

    <p>-5</p> Signup and view all the answers

    If a diver is at a depth of -15 meters and moves 7 meters towards the surface, what is their new depth?

    <p>-8 meters</p> Signup and view all the answers

    What is the result of adding 2 and -3?

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

    If a mountain has a height of 2500 meters above the surrounding ocean, and the ocean is at a depth of -3000 meters, what is the difference in height between the mountain and the ocean?

    <p>5000 meters</p> Signup and view all the answers

    What is the result of raising $a^m$ to the power of $n$, where $a$ is a non-zero integer and $m$ and $n$ are integers?

    <p>$a^{m imes n}$</p> Signup and view all the answers

    What is the result of dividing $a^m$ by $a^n$, where $a$ is a non-zero integer and $m$ and $n$ are integers?

    <p>$a^{m-n}$</p> Signup and view all the answers

    What is the result of multiplying $a^m$ by $a^n$, where $a$ is a non-zero integer and $m$ and $n$ are integers?

    <p>$a^{m+n}$</p> Signup and view all the answers

    What is the result of converting $0.0003$ to scientific notation?

    <p>$3 imes 10^{-3}$</p> Signup and view all the answers

    What is the result of cubing the fraction $2/3$?

    <p>$8/27$</p> Signup and view all the answers

    What is the result of multiplying $(-2)^3$ by $(-2)^2$?

    <p>$-32$</p> Signup and view all the answers

    What is the result of adding $2^3$ to $3^2$?

    <p>$13$</p> Signup and view all the answers

    What is the result of dividing $(-3)^4$ by $(-3)^2$?

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

    What is the result of subtracting $2^3$ from $3^3$?

    <p>$13$</p> Signup and view all the answers

    What is the result of multiplying $(2^3)$ by $(3^2)$?

    <p>$108$</p> Signup and view all the answers

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