Q. What is the simplified form of (2^3)^2? (2023)
-
A.
2^5
-
B.
2^6
-
C.
2^7
-
D.
2^8
Solution
Using the property of exponents (a^m)^n = a^(m*n), we have (2^3)^2 = 2^(3*2) = 2^6.
Correct Answer:
B
— 2^6
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Q. What is the simplified form of (x^2 * y^3)^(2)? (2023)
-
A.
x^4 * y^6
-
B.
x^2 * y^3
-
C.
x^6 * y^4
-
D.
x^5 * y^3
Solution
Using the power of a product property, we have (x^2 * y^3)^(2) = x^(2*2) * y^(3*2) = x^4 * y^6.
Correct Answer:
A
— x^4 * y^6
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Q. What is the simplified form of (x^3 * x^2) / x^4? (2023)
-
A.
x^1
-
B.
x^0
-
C.
x^2
-
D.
x^5
Solution
Using the property of exponents, we have (x^3 * x^2) / x^4 = x^(3+2-4) = x^1.
Correct Answer:
A
— x^1
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Q. What is the value of (5^0 + 5^1 + 5^2)? (2023)
Solution
Calculating each term, we have 5^0 = 1, 5^1 = 5, and 5^2 = 25. Therefore, 1 + 5 + 25 = 31.
Correct Answer:
C
— 15
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Q. What is the value of (5^3 * 5^2) / 5^4?
Solution
Using the property of exponents, (5^3 * 5^2) = 5^(3+2) = 5^5. Thus, (5^5) / (5^4) = 5^(5-4) = 5^1 = 5.
Correct Answer:
B
— 1
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Q. What is the value of 5^(-2)?
-
A.
0.04
-
B.
0.2
-
C.
2.5
-
D.
25
Solution
5^(-2) is equal to 1/(5^2) = 1/25 = 0.04.
Correct Answer:
A
— 0.04
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Q. What is the value of 5^(2) * 5^(3) / 5^(4)? (2023)
Solution
Using the property of exponents, we have 5^(2 + 3 - 4) = 5^1 = 5.
Correct Answer:
A
— 5
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Q. What is the value of 5^(x+1) / 5^(x-1)? (2023)
-
A.
5^2
-
B.
5^0
-
C.
5^1
-
D.
5^(x+2)
Solution
Using the property of exponents a^m / a^n = a^(m-n), we have 5^(x+1) / 5^(x-1) = 5^((x+1)-(x-1)) = 5^2.
Correct Answer:
A
— 5^2
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Q. Which of the following expressions is equivalent to (2^3)^2?
-
A.
2^5
-
B.
2^6
-
C.
2^9
-
D.
2^1
Solution
Using the power of a power property, (a^m)^n = a^(m*n), we get 2^(3*2) = 2^6.
Correct Answer:
B
— 2^6
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Q. Which of the following expressions is equivalent to (x^3 * y^2)^2?
-
A.
x^6 * y^4
-
B.
x^5 * y^2
-
C.
x^3 * y^6
-
D.
x^2 * y^2
Solution
Using the power of a product rule, (x^3 * y^2)^2 = x^(3*2) * y^(2*2) = x^6 * y^4.
Correct Answer:
A
— x^6 * y^4
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Q. Which of the following expressions is equivalent to 3^(2x) * 3^(x+1)?
-
A.
3^(3x + 1)
-
B.
3^(2x + x + 1)
-
C.
3^(x + 2)
-
D.
3^(2x + 1)
Solution
Using the property of exponents that states a^m * a^n = a^(m+n), we combine the exponents: 2x + (x + 1) = 3x + 1.
Correct Answer:
A
— 3^(3x + 1)
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Q. Which of the following expressions represents the inverse of 4^x?
-
A.
4^(-x)
-
B.
1/4^x
-
C.
4^(1-x)
-
D.
Both 1/4^x and 4^(-x)
Solution
Both 1/4^x and 4^(-x) represent the inverse of 4^x.
Correct Answer:
D
— Both 1/4^x and 4^(-x)
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Q. Which of the following is NOT a property of exponents?
-
A.
a^(m+n) = a^m * a^n
-
B.
a^(m-n) = a^m / a^n
-
C.
a^m * b^m = (ab)^m
-
D.
a^m + b^m = (a+b)^m
Solution
The statement a^m + b^m = (a+b)^m is not a property of exponents; it is only true for m=1.
Correct Answer:
D
— a^m + b^m = (a+b)^m
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Q. Which of the following is the correct simplification of (x^2y^3)/(xy^2)?
-
A.
x^(2-1)y^(3-2)
-
B.
x^1y^1
-
C.
x^2y^5
-
D.
x^3y^1
Solution
Using the quotient rule for exponents, (x^2y^3)/(xy^2) simplifies to x^(2-1)y^(3-2) = xy.
Correct Answer:
A
— x^(2-1)y^(3-2)
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Q. Which of the following is the correct simplification of (x^3 * y^2) / (x^2 * y)?
-
A.
x^(3-2) * y^(2-1)
-
B.
x^(5) * y^(1)
-
C.
x^(1) * y^(1)
-
D.
x^(1) * y^(3)
Solution
Using the property of exponents for division, we subtract the exponents: x^(3-2) * y^(2-1) = x^1 * y^1.
Correct Answer:
A
— x^(3-2) * y^(2-1)
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Q. Which of the following is the correct simplification of (x^3 * y^2)^(2)?
-
A.
x^6 * y^4
-
B.
x^5 * y^2
-
C.
x^3 * y^2
-
D.
x^2 * y^3
Solution
Using the power of a product property, (a*b)^n = a^n * b^n, we get (x^3)^2 * (y^2)^2 = x^6 * y^4.
Correct Answer:
A
— x^6 * y^4
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Q. Which of the following is the correct simplification of (x^3y^2)^2?
-
A.
x^6y^4
-
B.
x^5y^2
-
C.
x^3y^2
-
D.
x^2y^3
Solution
Using the power of a product property, (x^3y^2)^2 = x^(3*2)y^(2*2) = x^6y^4.
Correct Answer:
A
— x^6y^4
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Q. Which of the following is the result of (2^3)^2?
-
A.
2^5
-
B.
2^6
-
C.
2^7
-
D.
2^8
Solution
Using the power of a power property, (a^m)^n = a^(m*n), we get (2^3)^2 = 2^(3*2) = 2^6.
Correct Answer:
B
— 2^6
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Q. Which of the following is the result of (x^2y^3)^2?
-
A.
x^4y^6
-
B.
x^2y^3
-
C.
x^2y^6
-
D.
x^4y^3
Solution
Using the power of a power property, we multiply the exponents: (x^2)^2 = x^4 and (y^3)^2 = y^6.
Correct Answer:
A
— x^4y^6
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Q. Which of the following is the result of simplifying (2^3)^2?
-
A.
2^5
-
B.
2^6
-
C.
2^7
-
D.
2^8
Solution
Using the power of a power property, (a^m)^n = a^(m*n), we get (2^3)^2 = 2^(3*2) = 2^6.
Correct Answer:
B
— 2^6
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Q. Which of the following is true about the expression 2^(x+y)?
-
A.
It can be expressed as 2^x + 2^y.
-
B.
It can be expressed as 2^x * 2^y.
-
C.
It is always greater than 2.
-
D.
It is equal to 2 when x and y are both 0.
Solution
Using the property of exponents, 2^(x+y) = 2^x * 2^y.
Correct Answer:
B
— It can be expressed as 2^x * 2^y.
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Q. Which of the following is true for the expression 2^(x+1) / 2^(x-1)? (2023)
-
A.
2^2
-
B.
2^0
-
C.
2^1
-
D.
2^3
Solution
Using the property of exponents, we have 2^(x+1 - (x-1)) = 2^(x+1-x+1) = 2^2.
Correct Answer:
C
— 2^1
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Q. Which of the following is true for the expression 2^(x+3) = 8? (2023)
-
A.
x = 1
-
B.
x = 2
-
C.
x = 3
-
D.
x = 0
Solution
Since 8 can be expressed as 2^3, we have 2^(x+3) = 2^3, thus x + 3 = 3, leading to x = 0.
Correct Answer:
A
— x = 1
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Q. Which of the following is true for the expression 4^(x+1) = 16? (2023)
-
A.
x = 1
-
B.
x = 2
-
C.
x = 3
-
D.
x = 0
Solution
Since 16 can be expressed as 4^2, we have 4^(x+1) = 4^2, leading to x + 1 = 2, thus x = 1.
Correct Answer:
A
— x = 1
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Q. Which of the following represents the expression 10^(3x) in terms of its base?
-
A.
1000^x
-
B.
100^x
-
C.
10^x * 10^x * 10^x
-
D.
10^(x^3)
Solution
10^(3x) can be rewritten as (10^3)^x = 1000^x.
Correct Answer:
A
— 1000^x
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Q. Which of the following represents the expression 4^(3/2)?
Solution
4^(3/2) can be rewritten as (2^2)^(3/2) = 2^(2*3/2) = 2^3 = 8.
Correct Answer:
A
— 8
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Q. Which of the following statements about exponents is false?
-
A.
a^m * a^n = a^(m+n)
-
B.
a^m / a^n = a^(m-n)
-
C.
a^0 = 0
-
D.
a^(-n) = 1/a^n
Solution
The statement a^0 = 0 is false; in fact, a^0 = 1 for any non-zero a.
Correct Answer:
C
— a^0 = 0
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Q. Which of the following statements about exponents is incorrect?
-
A.
a^(m+n) = a^m * a^n
-
B.
a^(m-n) = a^m / a^n
-
C.
a^m * b^m = (ab)^m
-
D.
a^m + a^n = a^(m+n)
Solution
The statement a^m + a^n = a^(m+n) is incorrect; addition of exponents does not apply in this manner.
Correct Answer:
D
— a^m + a^n = a^(m+n)
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Q. Which of the following statements about negative exponents is correct?
-
A.
They indicate a reciprocal of the base raised to the positive exponent.
-
B.
They always result in a negative number.
-
C.
They can only be applied to integers.
-
D.
They are not applicable in real number systems.
Solution
Negative exponents indicate the reciprocal of the base raised to the positive exponent.
Correct Answer:
A
— They indicate a reciprocal of the base raised to the positive exponent.
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Q. Which of the following statements is true regarding the expression 2^(x+y)?
-
A.
It can be expressed as 2^x + 2^y.
-
B.
It can be expressed as 2^x * 2^y.
-
C.
It is always greater than 1.
-
D.
It is equal to x + y.
Solution
The property of exponents states that a^(m+n) = a^m * a^n.
Correct Answer:
B
— It can be expressed as 2^x * 2^y.
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