Section 2.3 - Power Of A Power
Complete the following questions
- 1.
Express (5^5)^3 as a power with a single exponent
- A.
5^2
- B.
5^8
- C.
5^15
- D.
5^125
Correct Answer
C. 5^15Explanation
To express (5^5)^3 as a power with a single exponent, we need to multiply the exponents. So, (5^5)^3 can be rewritten as 5^(5*3), which simplifies to 5^15.Rate this question:
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- 2.
Express (4^4)^4 as a power with a single exponent
- A.
4^256
- B.
4^16
- C.
4^8
- D.
4^0
Correct Answer
B. 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?
- A.
(a^m)^n = a^(m+n)
- B.
(a^m)^n = a^(m-n)
- C.
(a^m)^n = a^(m^n)
- D.
(a^m)^n = a^(mn)
Correct Answer
D. (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)
- A.
4^5 or 1024
- B.
4^6 or 4096
- C.
4^7 or 16 384
- D.
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)
- A.
3^2 or 9
- B.
3^3 or 27
- C.
3^4 or 81
- D.
3^5 or 243
Correct Answer
C. 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]
- A.
Z^17
- B.
Z^28
- C.
Z^70
- D.
Z^192
Correct Answer
B. 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)]
- A.
R^2
- B.
R^3
- C.
R^12
- D.
R^16
Correct Answer
D. 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
- A.
3^2
- B.
3^4
- C.
3^12
- D.
3^16
Correct Answer
B. 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
- A.
-625(n^5)
- B.
-625(n^6)
- C.
625(n^5)
- D.
625(n^6)
Correct Answer
D. 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
- A.
4w^8
- B.
4w^4
- C.
16w^8
- D.
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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