Challenge Yourself: Indices Test

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| By Catherine Halcomb
Catherine Halcomb
Community Contributor
Quizzes Created: 1442 | Total Attempts: 6,630,299
| Attempts: 28
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  • 1/10 Questions

    B3 x b4

    • B7
    • B34
    • B12
    • B
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About This Quiz

Think you've mastered the laws of indices? Ready to tackle exponents, radicals, and those tricky fractional powers? Then put your knowledge to the test with our challenging "Indices Test"! This quiz is designed to push your understanding of indices to the limit. We'll cover a range of topics, including simplifying expressions, applying the laws of indices, working with fractional See moreand negative indices, and solving equations with indices.

This Indices test is designed to sharpen your skills and boost your confidence. You'll get instant feedback on your answers and helpful explanations to solidify your understanding. If you're a student preparing for exams, a math enthusiast seeking a challenge, or just someone who wants to brush up on their algebra skills, this quiz is for you.

Challenge Yourself: Indices Test - Quiz

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  • 2. 

    Is (a4)5  is a9 true or false?

    • True

    • False

    Correct Answer
    A. False
    Explanation
    When raising a power to another power, you multiply the exponents. Here, (a^4)^5 becomes a^(4x5) = a^20. Since a^20 is not equal to a^9, the statement is false. Always remember to multiply exponents when a power is raised to another power.

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  • 3. 

    X0 is equal to ........

    Correct Answer
    1
    Explanation
    Any non-zero number raised to the power of 0 is always 1. For example, x^0 = x^(n-n) = x^(n)/x^(n) = 1. This rule works for all numbers except 0, as 0^0 is undefined.

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  • 4. 

    R3 x r2 x 2

    • 2r2

    • 2r5

    • 2r6

    • R6

    Correct Answer
    A. 2r5
    Explanation
    First, combine r^3 and r^2 by adding their powers since the base is the same. This gives r^(3+2) = r^5. Multiply by 2, which remains a coefficient. The final answer is 2r^5. The 2 does not affect the exponent of r.

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  • 5. 

    Is (8-2)3 is 8-6 true or false?

    • True

    • False

    Correct Answer
    A. True
    Explanation
    When raising a power to another power, multiply the exponents. Here, (8^-2)3 becomes 8^((-2)x3) = 8^-6. This follows the rule of multiplying exponents when a power is raised to another power.

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  • 6. 

    (-5)4

    • -625

    • 625

    • -125

    • 125

    Correct Answer
    A. 625
    Explanation
    Raising a negative number to an even power always results in a positive value. Here, (-5)^4 = (-5) x (-5) x (-5) x (-5) = 625. Negative signs cancel out in pairs. If the power was odd, the result would be negative.

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  • 7. 

    4n x 42n-1

    • 42n-1

    • 43n-n

    • 43n-1

    • 43n-3

    Correct Answer
    A. 43n-1
    Explanation
    Multiply terms with the same base by adding their powers. Here, the powers are n and 2n-1. Add them: n + (2n-1) = 3n-1. So, 4^n x 4^2n-1 = 4^3n-1. The base remains 4 throughout.

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  • 8. 

    (p3q-5)-2

    • P6q10

    • P-6q10

    • P-6q-10

    • -2p3q-5

    Correct Answer
    A. P-6q10
    Explanation
    Apply the -2 power to both terms. For p^3, multiply 3 x -2 to get p^-6. For q^-5, multiply -5 x -2 to get q^10. The result is p^-6q^10. Negative exponents mean reciprocal values if simplified further.

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  • 9. 

    C2n+3 x c3n-1

    • C-n+1

    • C5n+4

    • Cn+2

    • C5n+2

    Correct Answer
    A. C5n+2
    Explanation
    Add the exponents for the base c. Here, (2n+3) + (3n-1) = 5n+2. So, c^2n+3 x c^3n-1 = c5n+2. The base c does not change, and only the powers are added together.

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  • 10. 

    5 x a2 x a3 x a-1 x 2

    • 5a6

    • 10a4

    • 10a5

    • 5a4

    Correct Answer
    A. 10a4
    Explanation
    Combine the powers of a by adding the exponents: 2 + 3 - 1 = 4. This gives a^4. Multiply the constants 5 and 2 to get 10. The final answer is 10a^4. The coefficients and exponents are handled separately.

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  • Current Version
  • Jan 02, 2025
    Quiz Edited by
    ProProfs Editorial Team
  • Oct 25, 2024
    Quiz Created by
    Catherine Halcomb
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