Section 2.3 - Power Of A Power
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Express (5^5)^3 as a power with a single exponent
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5^2
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5^8
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5^15
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5^125
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This quiz focuses on the exponentiation rule where powers are raised to other powers, illustrated through problems simplifying expressions like (5^5)^3 and (4^4)^4.
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- 2.
Express (4^4)^4 as a power with a single exponent
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4^256
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4^16
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4^8
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4^0
Correct Answer
A. 4^16Explanation
To express (4^4)^4 as a power with a single exponent, we need to multiply the exponents. In this case, the exponent 4 is being raised to the power of 4. So, 4^4 is 256. Therefore, (4^4)^4 is equal to 256^4, which simplifies to 4^16.Rate this question:
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- 3.
Which of the following expression represents the Exponent Principle for Power of a Power?
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(a^m)^n = a^(m+n)
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(a^m)^n = a^(m-n)
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(a^m)^n = a^(m^n)
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(a^m)^n = a^(mn)
Correct Answer
A. (a^m)^n = a^(mn)Explanation
The correct answer is (a^m)^n = a^(mn). This expression represents the Exponent Principle for Power of a Power. According to this principle, when a power is raised to another power, we multiply the exponents. In this case, we have (a^m)^n, which means we have a base of 'a' raised to the power of 'm', and that entire expression is raised to the power of 'n'. So, we multiply the exponents and get a^(mn) as the final result.Rate this question:
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- 4.
Simplify (4^1)^2(4^3)
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4^5 or 1024
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4^6 or 4096
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4^7 or 16 384
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4^9 or 262 144
Correct Answer
A. 4^5 or 1024Explanation
The expression (4^1)^2(4^3) can be simplified by applying the exponent rules. First, we simplify the exponent (4^1)^2, which is equal to 4^2 or 16. Then, we multiply this result by 4^3, which is equal to 64. Therefore, the final result is 16 * 64 = 1024, which matches the first option.Rate this question:
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- 5.
Simplify [(3^3)^2] / (3^2)
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3^2 or 9
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3^3 or 27
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3^4 or 81
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3^5 or 243
Correct Answer
A. 3^4 or 81Explanation
The given expression can be simplified by using the exponent rule that states that when raising a power to another power, you multiply the exponents. Thus, (3^3)^2 can be simplified to 3^6. Dividing this by 3^2 gives us 3^4, which is equal to 81. Therefore, the correct answer is 81.Rate this question:
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- 6.
Simplify [(z^4)^3] [(z^8)^2]
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Z^17
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Z^28
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Z^70
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Z^192
Correct Answer
A. Z^28Explanation
The given expression can be simplified by applying the power of a power rule. First, we simplify each term inside the parentheses by multiplying the exponents. (z^4)^3 becomes z^12, and (z^8)^2 becomes z^16. Then, we multiply the two simplified terms together by adding the exponents. z^12 * z^16 equals z^28. Therefore, the correct answer is z^28.Rate this question:
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- 7.
Simplify [(r^6)^4] / [(r^8)]
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R^2
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R^3
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R^12
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R^16
Correct Answer
A. R^16Explanation
To simplify the given expression, we apply the exponent rule which states that when raising a power to another power, we multiply the exponents. In this case, we have (r^6)^4, which simplifies to r^24. Then, we divide r^24 by r^8, which gives us r^(24-8) = r^16. Therefore, the correct answer is r^16.Rate this question:
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- 8.
Simplify [(3^4)(3^3)]^2 / [(3^2)(3^3)]^2
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3^2
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3^4
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3^12
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3^16
Correct Answer
A. 3^4Explanation
The given expression can be simplified using the rules of exponents. When we multiply two numbers with the same base, we add their exponents. Therefore, [(3^4)(3^3)]^2 can be simplified to 3^(4+3)^2. Similarly, [(3^2)(3^3)]^2 can be simplified to 3^(2+3)^2. Simplifying further, we get 3^7^2 / 3^5^2. According to the rule of division, when we divide two numbers with the same base, we subtract their exponents. Therefore, 3^7^2 / 3^5^2 simplifies to 3^(7-5)^2 which equals 3^2.Rate this question:
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- 9.
Simplify[ (-5^2)(n^3) ]^2
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-625(n^5)
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-625(n^6)
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625(n^5)
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625(n^6)
Correct Answer
A. 625(n^6)Explanation
The expression (-5^2)(n^3) simplifies to (-25)(n^3). When we square this expression, we get (-25)^2(n^3)^2 which is equal to 625(n^6).Rate this question:
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- 10.
Simplify [(4w^2)]^5 / [(4^2)w]^2
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4w^8
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4w^4
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16w^8
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16w^4
Correct Answer
A. 4w^8Explanation
To simplify the expression, we can use the rule of exponents. First, we simplify the numerator by raising 4w^2 to the power of 5, which gives us (4^5)(w^10). Next, we simplify the denominator by raising (4^2)w to the power of 2, which gives us (4^4)(w^2). Finally, we divide the numerator by the denominator, which gives us (4^5)(w^10) / (4^4)(w^2). Simplifying further, we can cancel out the common factors of 4 and w^2, leaving us with (4^1)(w^8). Therefore, the simplified expression is 4w^8.Rate this question:
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Mar 19, 2023Quiz Edited by
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Feb 01, 2009Quiz Created by
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