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Quizzes > Mathematics

Rules of Exponents Quiz

Quick, free exponent quiz with instant results and feedback.

Editorial: Review CompletedCreated By: Nicoll CurtinUpdated Aug 26, 2025
Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art style math illustration featuring exponent rules negative exponents quiz design on sky blue background

This quiz helps you practice the rules of exponents, including zero and negative powers, with instant feedback to build speed and confidence. For wider review, try our exponents quiz or focus on multiplying powers with the product rule quiz. Build skills with the exponents practice quiz.

Simplify 3^2 * 3^4.
3^6
3^8
3^4
6^3
To multiply powers with the same base, you add their exponents: 2 + 4 = 6, giving 3^6. This avoids multiplying out each factor one by one. Recognizing common bases speeds up simplification. .
Simplify (x^3)^2.
x^5
x^9
x
x^6
The power of a power rule states (a^m)^n = a^(m·n). Here 3 · 2 = 6, so (x^3)^2 simplifies to x^6. This rule applies to any exponentiated exponent. .
Simplify 2^5 ÷ 2^2.
2^2
2^7
3^3
2^3
The quotient rule for exponents says a^m ÷ a^n = a^(m?n). Subtracting here gives 5 ? 2 = 3, so the result is 2^3. This rule avoids dividing out each power explicitly. .
What is the value of x^0 for any nonzero x?
0
Undefined
1
x
By definition, any nonzero base raised to the zero power equals 1. This follows from the quotient rule when dividing identical powers. Note that 0^0 is indeterminate, but x^0 = 1 when x ? 0. .
Simplify (ab)^3.
a b^3
a^3 b^3
a^2 b^2
a^3 b
The power of a product rule states (ab)^n = a^n b^n. Here n = 3, so each factor is raised to the third power. This rule distributes the exponent across the product. .
Evaluate (2^3 · 3^2)^0.
1
0
2^5
2^0 · 3^0
Any nonzero quantity raised to the zero power equals 1, regardless of its internal factors. Even combined expressions follow this rule. This stems from the pattern of decreasing exponents. .
Simplify 5^(?2).
1/25
?1/25
25
?25
A negative exponent indicates a reciprocal: a^(?n) = 1/a^n. Here 5^(?2) = 1/(5^2) = 1/25. It inverts the base and uses a positive exponent. .
Simplify (x^(?2) y^3)^2 ÷ (x y^(?1))^3.
y^9 / x^7
y^6 / x^5
x^7 / y^9
x^(?7) y^9
First apply the power-of-a-power rule: (x^(?2) y^3)^2 = x^(?4) y^6. Next, (x y^(?1))^3 = x^3 y^(?3). Dividing subtracts exponents: x^(?4?3) = x^(?7) and y^(6?(?3)) = y^9, giving x^(?7) y^9, which is y^9/x^7. .
0
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Study Outcomes

  1. Understand Exponent Laws -

    Grasp the foundational rules of exponents, including product, quotient, and power laws, to confidently tackle any exponent rules quiz.

  2. Apply Product and Quotient Rules -

    Use exponent laws practice to multiply and divide expressions with the same base, simplifying complex terms in a math exponent quiz context.

  3. Simplify Power Expressions -

    Demonstrate mastery of power-of-a-power and power-of-a-product rules to reduce expressions quickly during a rules of exponents test.

  4. Manipulate Negative and Zero Exponents -

    Convert and simplify expressions featuring negative and zero exponents, ensuring accuracy in any exponent rules practice scenario.

  5. Analyze Real-World Problems -

    Interpret and solve real-life exponent questions, improving problem-solving skills and boosting confidence on a math exponent quiz.

  6. Evaluate Quiz Performance -

    Review instant scoring feedback to identify strengths and areas for review, optimizing your study plan for future exponent laws practice.

Cheat Sheet

  1. Product Rule -

    The product rule states that when you multiply like bases, you add their exponents: am·an=am+n. For example, 23·24=27=128. Mnemonic trick: "Add the exponents when your bases are best friends."

  2. Quotient Rule -

    To divide like bases, subtract the exponents: am/an=am - n (with a≠0). Example: 57/52=55=3125. Remember "Upstairs minus downstairs" to keep it straight.

  3. Power of a Power -

    When an exponentiated term is raised to another power, multiply the exponents: (am)n=am·n. For instance, (32)4=38=6,561. Many textbooks like MIT OCW highlight this as "multiply to magnify."

  4. Power of a Product -

    The power of a product distributes: (ab)n=an·bn. Example from Harvard's pre-calculus notes: (2·3)2=22·32=36. Think "each factor gets its own exponent" for easy recall.

  5. Zero & Negative Exponents -

    An exponent of zero equals one: a0=1 (a≠0), and negative exponents flip the base: a - n=1/an. For example, 4 - 2=1/16. A popular mantra is "zero gives one, negatives take (you) back."

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