Exponents and Divison Quiz
Connections Academy 8th Grade
Please only use this to check your answers.
All of the equations that have / are fractions.
1. Write each expression using a single exponent.
x⁹/ x²
A. x¹¹
B. x⁷ ***
C. 7
D. x⁵
2. Write each expression using a single exponent.
h¹⁴/ h⁵
A. h⁹
B. 1/h⁹
C. h¹⁹
D. h⁹ ***
Simplify each expression
3. 4⁴/4⁶
A. -16
B. 16
C. 1/16 ***
D. -1/16
4. 5⁰
A. 0
B. 5
C. 1 ***
D. -5
5. Replace the ___ with <,> or = to make a true statement.
7⁴/ 7² _____ 49
A. <
B. >
C. = ***
D. none of the above
Multiply the following polynomials.
6. -2r(8r + 5)
A. -16r² + 5
B. -16r² + 10
C. -16r² - 10r ***
D. -16r² - 10
7. 4a(a² + 7a + 4)
A. 4a + 28a² + 16a
B. 4a³ + 28a² + 16a ***
C. 4a³ + 44a
D. 44a⁴
8. (2y - 3)(3y - 2)
A. 6y² - 13y + 6 ***
B. 6y² - 13y - 6
C. 6y² + 13y - 6
D. 6y² + 13y + 6
1. B. x⁷
2. D. h⁹
3. C. 1/16
4. C. 1
5. C. =
6. C. -16r² - 10r
7. B. 4a³ + 28a² + 16a
8. A. 6y² - 13y + 6
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To solve the given quiz questions, let's go step by step:
1. Write each expression using a single exponent.
To simplify x⁹/ x², you subtract the exponents. So, x⁹/ x² is equal to x⁹-² = x⁷. Therefore, the answer is B. x⁷.
2. Write each expression using a single exponent.
To simplify h¹⁴/ h⁵, you subtract the exponents. So, h¹⁴/ h⁵ is equal to h¹⁴-⁵ = h⁹. Therefore, the answer is D. h⁹.
Simplify each expression:
3. 4⁴/4⁶
To simplify 4⁴/4⁶, you subtract the exponents. So, 4⁴/4⁶ is equal to 4⁴-⁶ = 1/4² = 1/16. Therefore, the answer is C. 1/16.
4. 5⁰
Any number raised to the power of zero is equal to 1. So, 5⁰ = 1. Therefore, the answer is C. 1.
Replace the ___ with <, > or = to make a true statement:
5. 7⁴/ 7² _____ 49
To compare 7⁴/ 7² and 49, let's simplify the first expression. 7⁴/ 7² is equal to 7⁴-² = 7². And we can see that 7² is equal to 49. Thus, the statement is 7⁴/ 7² = 49, which means they are equal. Therefore, the answer is C. =.
Multiply the following polynomials:
6. -2r(8r + 5)
To multiply -2r with (8r + 5), you have to distribute the -2r to both terms inside the parentheses. -2r multiplied by 8r is -16r², and -2r multiplied by 5 is -10r. So, the multiplied polynomial is -16r² - 10r. Therefore, the answer is C. -16r² - 10r.
7. 4a(a² + 7a + 4)
To multiply 4a with (a² + 7a + 4), you have to distribute the 4a to each term inside the parentheses. 4a multiplied by a² is 4a³, 4a multiplied by 7a is 28a², and 4a multiplied by 4 is 16a. So, the multiplied polynomial is 4a³ + 28a² + 16a. Therefore, the answer is B. 4a³ + 28a² + 16a.
8. (2y - 3)(3y - 2)
To multiply (2y - 3) with (3y - 2), you have to distribute each term from the first polynomial to each term in the second polynomial. (2y multiplied by 3y) is 6y², (2y multiplied by -2) is -4y, (-3 multiplied by 3y) is -9y, and (-3 multiplied by -2) is 6. So, the multiplied polynomial is 6y² - 13y + 6. Therefore, the answer is A. 6y² - 13y + 6.
Note: The answers marked with *** are correct.