Section 2.3 - Power Of A Power

Reviewed by Editorial Team
The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.
Learn about Our Editorial Process
| By Seixeiroda
S
Seixeiroda
Community Contributor
Quizzes Created: 41 | Total Attempts: 30,315
| Attempts: 259
SettingsSettings
Please wait...
  • 1/10 Questions

    Express (5^5)^3 as a power with a single exponent

    • 5^2
    • 5^8
    • 5^15
    • 5^125
Please wait...
About This Quiz

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.

Exponents Quizzes & Trivia

Quiz Preview

  • 2. 

    Express (4^4)^4 as a power with a single exponent

    • 4^256

    • 4^16

    • 4^8

    • 4^0

    Correct Answer
    A. 4^16
    Explanation
    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:

  • 3. 

    Which of the following expression represents the Exponent Principle for Power of a Power?

    • (a^m)^n = a^(m+n)

    • (a^m)^n = a^(m-n)

    • (a^m)^n = a^(m^n)

    • (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:

  • 4. 

    Simplify (4^1)^2(4^3)

    • 4^5 or 1024

    • 4^6 or 4096

    • 4^7 or 16 384

    • 4^9 or 262 144

    Correct Answer
    A. 4^5 or 1024
    Explanation
    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:

  • 5. 

    Simplify [(3^3)^2] / (3^2)

    • 3^2 or 9

    • 3^3 or 27

    • 3^4 or 81

    • 3^5 or 243

    Correct Answer
    A. 3^4 or 81
    Explanation
    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:

  • 6. 

    Simplify [(r^6)^4] / [(r^8)]

    • R^2

    • R^3

    • R^12

    • R^16

    Correct Answer
    A. R^16
    Explanation
    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:

  • 7. 

    Simplify  [(3^4)(3^3)]^2  /  [(3^2)(3^3)]^2

    • 3^2

    • 3^4

    • 3^12

    • 3^16

    Correct Answer
    A. 3^4
    Explanation
    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:

  • 8. 

    Simplify [(z^4)^3] [(z^8)^2]

    • Z^17

    • Z^28

    • Z^70

    • Z^192

    Correct Answer
    A. Z^28
    Explanation
    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:

  • 9. 

    Simplify [(4w^2)]^5 / [(4^2)w]^2

    • 4w^8

    • 4w^4

    • 16w^8

    • 16w^4

    Correct Answer
    A. 4w^8
    Explanation
    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:

  • 10. 

    Simplify[ (-5^2)(n^3) ]^2

    • -625(n^5)

    • -625(n^6)

    • 625(n^5)

    • 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:

Quiz Review Timeline (Updated): Mar 19, 2023 +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

  • Current Version
  • Mar 19, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Feb 01, 2009
    Quiz Created by
    Seixeiroda
Back to Top Back to top
Advertisement
×

Wait!
Here's an interesting quiz for you.

We have other quizzes matching your interest.