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 (B)</p> Signup and view all the answers

What is a closed number sentence?

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

What is the Distributive Property of Multiplication?

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

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

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

What is the product of two negative integers?

<p>Positive (A)</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 (C)</p> Signup and view all the answers

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

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

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

<p>A negative integer (A)</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 (B)</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 (D)</p> Signup and view all the answers

What is the purpose of scientific notation?

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

What is the Distributive Property of multiplication?

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

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

<p>Zero (D)</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 (C)</p> Signup and view all the answers

What is the effect of subtracting a negative integer?

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

What type of equation has some unknown numbers?

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

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

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

What is the purpose of the temperature rise problem?

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

What happens when you subtract a negative integer?

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

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

<p>x + 2 = 7 (D)</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 (A)</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 (A)</p> Signup and view all the answers

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

<p>&lt; (C)</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 (C)</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. (D)</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. (B)</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 (B)</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. (A)</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; (D)</p> Signup and view all the answers

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

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

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

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

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

<p>Zero (B)</p> Signup and view all the answers

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

<p>8 (D)</p> Signup and view all the answers

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

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

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

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

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

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

What is the result of converting 3000 to scientific notation?

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

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

<p>5 (A)</p> Signup and view all the answers

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

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

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

<p>15 (D)</p> Signup and view all the answers

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

<p>9 (C)</p> Signup and view all the answers

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

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

What is the result of subtracting 5 from -3?

<p>-8 (A)</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. (B)</p> Signup and view all the answers

What is the additive inverse of 5?

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

What is the result of adding 3 and -5?

<p>-2 (C)</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;= (D)</p> Signup and view all the answers

What is the result of subtracting -3 from 2?

<p>5 (D)</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. (D)</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. (C)</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 (B)</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. (A)</p> Signup and view all the answers

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

<p>&gt; (A)</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. (D)</p> Signup and view all the answers

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

<p>Distributive Property (A)</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. (D)</p> Signup and view all the answers

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

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

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

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

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

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

What is the result of converting 4500 to scientific notation?

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

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

<p>Compare the exponents first (B)</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 (C)</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 (C)</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 (D)</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 (A)</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 (B)</p> Signup and view all the answers

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

<p>Zero (D)</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 (C)</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 (A)</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 (D)</p> Signup and view all the answers

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

<p>A positive integer (A)</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 (B)</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>$a^{m+n}$ (D)</p> Signup and view all the answers

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

<p>Always positive (A)</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>$a^{m-n}$ (B)</p> Signup and view all the answers

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

<p>Always positive (C)</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 (A)</p> Signup and view all the answers

What is the result of squaring a negative fraction?

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

What is the result of converting 0.0003 to scientific notation?

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

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

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

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

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

What is the result of cubing a negative fraction?

<p>Always negative (B)</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 (D)</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 (D)</p> Signup and view all the answers

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

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

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

<p>≥ (C)</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 (C)</p> Signup and view all the answers

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

<p>Zero (B)</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 (D)</p> Signup and view all the answers

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

<p>Zero (A)</p> Signup and view all the answers

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

<p>0 (C)</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 (D)</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 (A)</p> Signup and view all the answers

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

<p>≤ (A)</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 (A)</p> Signup and view all the answers

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

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

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

<p>0 (C)</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 (B)</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) (A)</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 (A)</p> Signup and view all the answers

What is the result of subtracting 3 from -2?

<p>-5 (C)</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 (B)</p> Signup and view all the answers

What is the result of adding 2 and -3?

<p>-1 (C)</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 (B)</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>$a^{m imes n}$ (A)</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>$a^{m-n}$ (D)</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>$a^{m+n}$ (C)</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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