Math Trivia: Algebra MCQ Exam!
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- 1.
Write the product of 52 x 54 as a single power.
- A.
106
- B.
56
- C.
256
- D.
58
Correct Answer
B. 56Explanation
To find the product of two numbers as a single power, you add the exponents. In this case, both numbers have a base of 2 and different exponents. 52 can be written as 2^2 and 54 can be written as 2^3. Adding the exponents gives us 2^5, which is equal to 32. Therefore, the product of 52 x 54 as a single power is 32.Rate this question:
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- 2.
Evaluate: (2+3)2 – (3-5)3
- A.
17
- B.
-85
- C.
16
- D.
33
Correct Answer
D. 33Explanation
The given expression can be simplified using the order of operations. First, we evaluate the parentheses: (2+3) equals 5 and (3-5) equals -2. Then, we calculate the exponents: 5^2 equals 25 and -2^3 equals -8. Finally, we subtract -8 from 25, resulting in 33.Rate this question:
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- 3.
Write [(-7) x 2]5 as a product of powers.
- A.
(-7)5 x 25
- B.
(-7)5 + 25
- C.
(-5)5
- D.
5(-7) x 2
Correct Answer
A. (-7)5 x 25Explanation
The given expression [(-7) x 2]5 can be simplified by first performing the multiplication (-7) x 2, which equals -14. Then, raising -14 to the power of 5 gives the final result of (-7)5. Therefore, the expression can be written as (-7)5 x 25.Rate this question:
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- 4.
Evaluate: - (100)7
- A.
-7
- B.
1
- C.
7
- D.
-1
Correct Answer
D. -1Explanation
When evaluating the expression - (100)7, we start by multiplying 100 by 7, which gives us 700. Then, since there is a negative sign in front of the expression, we change the sign of the result to -700. Therefore, the correct answer is -700.Rate this question:
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- 5.
Simplify the following: x2x3
- A.
X3
- B.
X6
- C.
X2
- D.
X5
Correct Answer
D. X5Explanation
The given expression x2x3 can be simplified by adding the exponents of x, which gives us x5. Therefore, the answer is x5.Rate this question:
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- 6.
Write the base of −(−6)5
- A.
6
- B.
-6
- C.
-6 x 5
- D.
5
Correct Answer
B. -6Explanation
The base of -(-6)5 is -6.Rate this question:
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- 7.
Write the quotient of 68 / 64 as a single power.
- A.
64
- B.
2
- C.
62
- D.
612
Correct Answer
A. 64Explanation
To find the quotient of 68 divided by 64, we divide the numerator (68) by the denominator (64). The quotient is 1 with a remainder of 4. Therefore, the fraction 68/64 can be simplified to 1 and 4/64. Since 4/64 can be simplified further to 1/16, the final simplified form of 68/64 is 1 + 1/16.Rate this question:
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- 8.
Find n so that the equation is true: (53)n = 518
- A.
N=6
- B.
N =15
- C.
N = 13
- D.
Infinitely many solution
Correct Answer
A. N=6Explanation
To find the value of n that makes the equation true, we need to solve the equation (53)n = 518. By evaluating the powers of 53, we find that 53^6 = 113,379,904, which is not equal to 518. Therefore, n=6 is not the correct answer.Rate this question:
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- 9.
Using the rules of exponents, simplify the following expression. Your answer should be in exponential form. 73 . 56 /7 . 52
- A.
73 . 52
- B.
74 . 53
- C.
72 . 54
- D.
73 . 54
Correct Answer
C. 72 . 54Explanation
The expression can be simplified using the rule of exponents that states "a^m . a^n = a^(m+n)". In this case, we have 73 . 56 / 7 . 52. We can simplify this by adding the exponents of 7 and 5, which gives us 72. Then, we can multiply the exponents of 3 and 2, which gives us 54. Therefore, the simplified expression in exponential form is 72 . 54.Rate this question:
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- 10.
Evaluate: [(-z)5]4
- A.
-z20
- B.
Z9
- C.
Z20
- D.
-z9
Correct Answer
C. Z20Explanation
The expression (-z)5 means that the value of z is multiplied by -1 five times. So, when we evaluate [(-z)5]4, we are multiplying the result of (-z)5 by 4. Since (-z)5 is equal to -z^5, the expression becomes -z^5 * 4. This can be simplified to -4z^5. Therefore, the correct answer is -z20.Rate this question:
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- 11.
Find the value of the polynomial when x = - 3; 2x3- 5x2 +6x - 7
- A.
-24
- B.
24
- C.
-34
- D.
34
Correct Answer
C. -34Explanation
When we substitute x = -3 into the polynomial 2x^3 - 5x^2 + 6x - 7, we get:
2(-3)^3 - 5(-3)^2 + 6(-3) - 7
= 2(-27) - 5(9) - 18 - 7
= -54 - 45 - 18 - 7
= -124
Therefore, the value of the polynomial when x = -3 is -124.Rate this question:
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- 12.
Evaluate: 3x4 + xy - 5x - y for x = 2, y = 3
- A.
38
- B.
39
- C.
40
- D.
41
Correct Answer
D. 41Explanation
The given expression is 3x4 + xy - 5x - y. Substituting x = 2 and y = 3 into the expression, we get 3(2^4) + 2(3) - 5(2) - 3. Simplifying this expression, we have 3(16) + 6 - 10 - 3 = 48 + 6 - 10 - 3 = 41. Therefore, the correct answer is 41.Rate this question:
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- 13.
Solve: - 2(x+1)2 + 2 for x = 1
- A.
-5
- B.
-6
- C.
-7
- D.
-8
Correct Answer
B. -6Explanation
To solve the equation, we substitute x = 1 into the equation and simplify. Plugging in x = 1, we have: -2(1+1)2 + 2. Simplifying further, we get: -2(2)2 + 2 = -2(4) + 2 = -8 + 2 = -6. Therefore, the correct answer is -6.Rate this question:
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- 14.
/2x+3/ - 7 for x = -5
- A.
-12
- B.
14
- C.
0
- D.
-14
Correct Answer
C. 0Explanation
The expression |2x+3| - 7 is being evaluated for x = -5. When x = -5, the expression becomes |2(-5)+3| - 7. Simplifying further, we have |-10+3| - 7, which becomes |-7| - 7. The absolute value of -7 is 7, so the expression becomes 7 - 7, which equals 0. Therefore, the correct answer is 0.Rate this question:
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- 15.
Evaluate: 3-4
- A.
1/3
- B.
1/81
- C.
1/27
- D.
1/9
Correct Answer
B. 1/81Explanation
The expression "3-4" simplifies to -1. When we divide -1 by 1/3, we can rewrite it as -1 * 3/1, which equals -3. Dividing -3 by 1/81 is the same as multiplying -3 by 81/1, resulting in -243. Therefore, the correct answer is 1/81.Rate this question:
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- 16.
Solve: (x-9) (x6) = ?
- A.
1/x3
- B.
1/x15
- C.
X3
- D.
X15/1
Correct Answer
A. 1/x3Explanation
The given expression (x-9)(x6) can be simplified by multiplying the terms inside the parentheses. When we multiply x by x6, we get x^7. Similarly, when we multiply -9 by x6, we get -9x^6. Therefore, the simplified expression is x^7 - 9x^6. However, this does not match any of the answer choices provided. Therefore, the correct answer is not available.Rate this question:
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- 17.
Evaluate: x4 - 5x2 - 2x + 1 for x = -2
- A.
-5
- B.
6
- C.
-7
- D.
8
Correct Answer
C. -7Explanation
To evaluate the expression x^4 - 5x^2 - 2x + 1 for x = -2, we substitute -2 into the expression. Replacing x with -2, we get (-2)^4 - 5(-2)^2 - 2(-2) + 1. Simplifying this expression, we have 16 - 5(4) + 4 + 1 = 16 - 20 + 4 + 1 = 1 - 20 + 4 + 1 = -19 + 5 = -14. Therefore, the correct answer is -14.Rate this question:
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- 18.
Evaluate: (2xy2/z4)3 =?
- A.
8x3y5/z7
- B.
8x3y6/z12
- C.
Y6/8x3z7
- D.
Y6/8x3z12
Correct Answer
B. 8x3y6/z12Explanation
The given expression is (2xy^2/z^4)^3. To simplify this expression, we raise each term inside the parentheses to the power of 3. Therefore, 2^3 = 8, (x)^3 = x^3, (y^2)^3 = y^6, and (z^4)^3 = z^12. Combining these terms, we get the simplified expression 8x^3y^6/z^12, which matches the given answer.Rate this question:
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- 19.
Simplify the following: (b5) (b2) (b7) = ?
- A.
B14
- B.
B15
- C.
B18
- D.
B22
Correct Answer
A. B14Explanation
The given expression involves multiplying three terms with the same base b. When multiplying terms with the same base, we add their exponents. In this case, the exponents are 5, 2, and 7. Adding these exponents gives us 14. Therefore, the simplified expression is b14.Rate this question:
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- 20.
In the given: (xy)4 = x4y4. What rules of exponents is being applied?
- A.
Power Rule
- B.
Power of a Quotient
- C.
Product Rule
- D.
Power of a Product
Correct Answer
C. Product RuleExplanation
The product rule of exponents is being applied in this case. The product rule states that when raising a product of two variables to a power, each variable is raised to that power individually. In the given equation, (xy)^4, both x and y are being raised to the power of 4 individually, resulting in x^4 * y^4.Rate this question:
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- 21.
Find -2x2 when x = -1
- A.
-3
- B.
-2
- C.
-1
- D.
2
Correct Answer
B. -2Explanation
When we substitute x = -1 into the expression -2x^2, we get -2(-1)^2 = -2(1) = -2. Therefore, the value of -2x^2 when x = -1 is -2.Rate this question:
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- 22.
Solve: 8r/r + 3r -1 where r = 3
- A.
15
- B.
16
- C.
17
- D.
18
Correct Answer
B. 16Explanation
The given expression is 8r/r + 3r - 1. By substituting r = 3 into the expression, we get 8(3)/3 + 3(3) - 1. Simplifying this further, we have 24/3 + 9 - 1, which equals 8 + 9 - 1. Finally, adding these numbers together, we get 16.Rate this question:
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- 23.
Simplify: (-2p3q5)2 = ?
- A.
4p6q10
- B.
8p6q7
- C.
4p5q10
- D.
6pq
Correct Answer
A. 4p6q10Explanation
The given expression (-2p3q5)2 can be simplified by raising each term inside the parentheses to the power of 2. This results in (-2)2 * p3*2 * q5*2 = 4p6q10.Rate this question:
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- 24.
Evaluate: (-3)0 = 1. What rule of exponent is being applied?
- A.
Quotient Rule
- B.
Negative Exponents
- C.
Zero Exponent
- D.
Power Rule
Correct Answer
C. Zero ExponentExplanation
The correct answer is Zero Exponent. The zero exponent rule states that any number raised to the power of zero is equal to 1. In this case, (-3) raised to the power of zero is equal to 1.Rate this question:
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- 25.
If you are raising a Power to an exponent, you multiply the exponents. This is the definition of what laws of exponents?
- A.
Product Rule
- B.
Quotient Rule
- C.
Power of a Power
- D.
Multiplying Power
Correct Answer
C. Power of a PowerExplanation
The explanation for the correct answer, Power of a Power, is that when raising a power to an exponent, you multiply the exponents. This means that if you have a base raised to an exponent, and that entire expression is raised to another exponent, you can simplify it by multiplying the exponents together. This is a fundamental rule in the laws of exponents and is known as the Power of a Power rule.Rate this question:
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- 26.
Evaluate: (39/35)-2
- A.
3-8
- B.
1/36
- C.
3-6
- D.
1/38
Correct Answer
D. 1/38Explanation
The expression (39/35)-2 can be simplified by first dividing 39 by 35, which equals 1.114. Then subtracting 2 from 1.114 gives us -0.886. Therefore, the correct answer is -0.886.Rate this question:
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- 27.
Evaluate the given algebraic expression: 2x3- 5x2 + 6x - 7
- A.
110
- B.
115
- C.
120
- D.
125
Correct Answer
A. 110Explanation
The given algebraic expression is 2x^3 - 5x^2 + 6x - 7. To evaluate this expression, we substitute the value of x with 5. So, when x = 5, the expression becomes 2(5)^3 - 5(5)^2 + 6(5) - 7. Simplifying this expression, we get 250 - 125 + 30 - 7 = 148. Since the given answer options do not match with the evaluated value, the correct answer is not available.Rate this question:
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- 28.
Simplify: (32) (34) = ?
- A.
36
- B.
38
- C.
729
- D.
6 561
Correct Answer
C. 729Explanation
To simplify the expression (32)(34), we can multiply the numbers together. 32 multiplied by 34 equals 1,088. However, since the question asks for a simplified answer, we need to find the square root of 1,088. The square root of 1,088 is equal to 32, so the simplified answer is 32.Rate this question:
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- 29.
Evaluate & Simplify: (-2)4 (-2)5 = ?
- A.
-29
- B.
29
- C.
512
- D.
-512
Correct Answer
D. -512Explanation
To evaluate this expression, we need to apply the exponent rules. The rule states that when multiplying two numbers with the same base, we add the exponents. In this case, we have (-2) raised to the power of 4 multiplied by (-2) raised to the power of 5. This can be simplified as (-2)^(4+5), which is equal to (-2)^9. Since the base is negative, the result will also be negative. Therefore, the correct answer is -512.Rate this question:
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- 30.
What is the value of x0 = ?
- A.
-1
- B.
0
- C.
1
- D.
2
Correct Answer
C. 1Explanation
The value of x0 is 1.Rate this question:
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Mar 20, 2023Quiz Edited by
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Oct 03, 2020Quiz Created by
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