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Simplifying Exponents and Algebraic Expressions with Exponents Quiz Algebra I
Questions and Answers
1.
Which choice represents the expression below as a single exponential expression?
6^{5} * 6^{3}
A.
6^8 * 6^8
B.
6^15
C.
6^2
D.
6^8
Correct Answer D. 6^8
Explanation The given expression, 65 * 63, can be represented as 6^8.
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2.
Which choice represents the expression below as a single exponential expression?
2^{11} * 2^{5}
A.
2^16 * 2^16
B.
2^16
C.
2^55
D.
2^6
Correct Answer B. 2^16
Explanation The correct answer is 2^16 because when multiplying two exponents with the same base, you add the exponents together. In this case, 2^16 * 2^16 can be simplified as 2^(16+16) = 2^32. However, none of the answer choices include 2^32, so the closest option is 2^16.
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3.
Which choice represents the expression below as a single exponential expression?
x^{9} * x^{7}
A.
X^16 * x^16
B.
X^63
C.
X^2
D.
X^16
Correct Answer D. X^16
Explanation The correct answer is x^16. This is because when multiplying two exponential expressions with the same base, you add the exponents. In this case, x^9 * x^7 can be rewritten as x^(9+7) which equals x^16.
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4.
Which choice represents the expression below as a single exponential expression?
y^{8} * y^{3}
A.
Y^5
B.
Y^24
C.
Y^11 * 4y11
D.
Y^11
Correct Answer D. Y^11
Explanation The expression y^8 * y^3 can be simplified by adding the exponents, which gives us y^(8+3) = y^11. Therefore, the correct answer is y^11.
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5.
The Multiplication Law of Exponents says that for any numbers b, n, and m, b^{n} * b^{m} = b^{n + m}.
A.
True
B.
False
Correct Answer A. True
Explanation The Multiplication Law of Exponents states that when multiplying two terms with the same base, you can add their exponents. This means that for any numbers b, n, and m, bn * bm is equal to bn + m. This is a fundamental rule in exponentiation and is used to simplify and solve equations involving exponents. Therefore, the given statement is true.
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6.
Use the Multiplication Law of Exponents to simplify the exponential expression below.
a^{100} * a^{300}
A.
A^300
B.
A^500
C.
A^30
D.
A^400
Correct Answer D. A^400
Explanation The Multiplication Law of Exponents states that when multiplying two exponential expressions with the same base, you can add the exponents. In this case, we are multiplying a^100 and a^300, both with the base "a". Therefore, we add the exponents 100 and 300, resulting in a^400.
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7.
Which choice represents the simplified exponential expression?
(5^{2})^{8}
A.
5^10
B.
5^-6
C.
5^16
D.
5
Correct Answer C. 5^16
Explanation The correct answer is 5^16 because it represents the exponential expression in its simplest form. The base number 5 is raised to the exponent 16, resulting in the value of 5 multiplied by itself 16 times. This is the simplest way to express the exponential expression without any further simplification.
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8.
Which choice represents the simplified exponential expression?
(x^{7})^{4}
A.
X^11
B.
X
C.
X^28
D.
X^3
Correct Answer C. X^28
Explanation The expression (x^7)^4 can be simplified by applying the power of a power rule, which states that when raising a power to another power, you multiply the exponents. Therefore, (x^7)^4 is equal to x^(7*4) or x^28.
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9.
Which choice represents the simplified exponential expression?
(z^{5})^{8}
A.
Z^-3
B.
Z
C.
Z^13
D.
Z^40
Correct Answer D. Z^40
Explanation The given expression (z^5)^8 can be simplified by multiplying the exponents, resulting in z^(5*8) = z^40. Therefore, the correct answer is z^40.
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10.
Which choice represents the simplified exponential expression?
(7^{4})^{6}
A.
7^24
B.
7^-2
C.
7
D.
7^10
Correct Answer A. 7^24
Explanation The given expression (74)6 can be simplified by multiplying 7 raised to the power of 4 with 6. This gives us 7^24, which is the same as the given answer.
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11.
Which choice represents the simplified exponential expression?
(s ^{-6})^{9}
A.
S
B.
S^3
C.
S^ -15
D.
S^ -54
Correct Answer D. S^ -54
Explanation The given expression, (s - 6)9, can be simplified by distributing the 9 to both terms inside the parentheses. This results in 9s - 54. Therefore, the simplified exponential expression is s^ -54.
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12.
Which choice represents the simplified exponential expression?
((-x)^{-3})^{7}
A.
(-x)^ -10
B.
(-x)^ -21
C.
-x
D.
(-x)^4
Correct Answer B. (-x)^ -21
Explanation The correct answer is (-x)^ -21. This expression represents the simplified form of the given exponential expression. The negative sign outside the parentheses indicates that the exponent applies to the entire term inside the parentheses. The base, -x, is raised to the power of -21, which means it is being inverted.
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13.
Correct Answer 3x^4z^5 / 2y^5
Explanation The given expression is a fraction with a numerator of 3x^4z^5 and a denominator of 2y^5. This means that there are 3x^4z^5 terms in the numerator and 2y^5 terms in the denominator. The expression cannot be simplified further because there are no like terms that can be combined. Therefore, the correct answer is 3x^4z^5 / 2y^5.