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Quizzes > Mathematics

Laws of Exponents Quiz: Check Your Understanding

Quick, free exponent rules quiz with instant feedback and helpful notes.

Editorial: Review CompletedCreated By: Mayur LankeshwarUpdated Aug 26, 2025
Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art illustrating a trivia quiz on exponent rules for high school math students.

This laws of exponents quiz helps you master the rules for multiplying, dividing, and simplifying powers while building speed and accuracy. Work through 20 questions with instant feedback and tips. If you want more practice, try our squares and cubes quiz, tackle a factoring polynomials quiz, or review with distributive property practice problems.

Simplify 3^4 * 3^2 using laws of exponents.
3^6 (add exponents when multiplying same base)
3^12
3^8
3^2
undefined
Simplify x^7 / x^3 for x != 0.
x^10
x^{-4}
x^3
x^4 (subtract exponents when dividing same base)
undefined
Simplify (y^5)^2.
y^7
y^{25}
y^10 (multiply exponents for a power of a power)
y^3
undefined
Simplify (2a)^3.
6a^3
2a^9
8a
8a^3 (power of a product)
undefined
Simplify (m/n)^3 for n != 0.
m^3/n^3 (power of a quotient)
mn^3
m/n^3
m^3/n
undefined
Evaluate a^0 for a != 0.
Undefined
1 (zero exponent rule)
0
a
undefined
Rewrite x^-3 without negative exponents for x != 0.
1/x^3 (negative exponent gives reciprocal)
-1/x^3
-x^3
-x^3
undefined
Express b^(3/2) in radical form for b >= 0.
bqrt(b^3) = (sqrt(b))^3 (i.e., sqrt(b^3))
b^2 sqrt(b)
cbrt(b^2)
sqrt(b)/b^3
undefined
Interpret -2^4 according to order of operations.
8
16
-16 (exponent before unary minus)
-8
undefined
Simplify (3x^2 y^-1)^2 with positive exponents only.
9x^4/y^2 (apply power to each factor)
6x^4/y^2
9x^2/y
9x^4y^2
undefined
Simplify (a/b)^-3 for a,b != 0.
b^{-3}/a^{-3}
a^3/b^3
a^3/b^3
(b/a)^3 (flip for negative exponent)
undefined
For 0 < r < 1, how does r^n change as n increases?
It oscillates between -1 and 1
It stays constant
It increases without bound
It decreases toward 0 (powers shrink for base between 0 and 1)
undefined
Solve for x given 3^(2x) = 3^8.
x = 2
x = 4 (equal bases imply equal exponents)
x = 8
x = 16
undefined
Which expression equals (r/s)^{1/2} for r,s >= 0 and s != 0?
sqrt(r/s^2)
r/sqrt(s)
sqrt(r)/s
sqrt(r)/sqrt(s) (root of a quotient)
undefined
Simplify (x^3 y^-2)/(x^-1 y) with positive exponents only.
x^4 / y^3 (subtract exponents by variable)
x^2 / y
x^3 y^{-3}
x^{-4} y^3
undefined
Simplify (ab^2)^3 / (a^2 b) with positive exponents only.
a^5 b
a^6 / b^3
a^2 b^2
a b^5 (a^{1} b^{6-1})
undefined
Simplify x^{5}y^{2} / (x^{-3}y^{-4}) with positive exponents only.
x^{5} y^{2}
x^{8} y^{6} (subtracting negatives adds)
x^{2} / y^{6}
x^{-8} y^{-6}
undefined
Choose the equivalent form of 16^(3/4).
16^{1/3}
(sqrt[4](16))^3 = 2^3 = 8
(sqrt(16))^{3/4}
sqrt(16^3) = 64
undefined
Simplify (x/y)^-2 x^3 y for x,y != 0, with positive exponents only.
x^5 / y^3 ((y/x)^2 times x^3 y)
x^3 y^3
x / y
y^3 / x^5
undefined
Simplify (4 a^-1 b^2)/(2 a^2 b^-3) with positive exponents only.
2a/b
2a^3/b^5
8b/a
2b^5/a^3 (combine coefficients and exponents)
undefined
0

Study Outcomes

  1. Apply exponent rules to simplify algebraic expressions.
  2. Analyze the properties of exponents in various mathematical contexts.
  3. Simplify products and quotients using exponent laws.
  4. Solve problems utilizing the power of a power rule.
  5. Demonstrate readiness for advanced tests through mastery of exponent concepts.

Laws of Exponents Cheat Sheet

  1. Product of Powers Rule - When you multiply numbers with the same base, just add the exponents to power up your answer! For example, 2^3 × 2^4 = 2^(3+4) = 2^7 makes calculation a breeze. Keep calm and sum exponents.
  2. Quotient of Powers Rule - Dividing exponents with the same base? Subtract one exponent from the other like a boss. For instance, 5^6 ÷ 5^2 = 5^(6−2) = 5^4, turning division into simple subtraction. Math never felt so easy!
  3. Power of a Power Rule - Raising a power to another power means multiplying the exponents. So (3^2)^4 = 3^(2×4) = 3^8, and voilà, you've leveled up your exponent game in one step. It's exponentception without the confusion!
  4. Power of a Product Rule - When a product is raised to an exponent, each factor gets its own exponent. For example, (2×3)^3 = 2^3 × 3^3 = 8 × 27 = 216, so you can distribute like a pro. No more guessing on products!
  5. Power of a Quotient Rule - Applying an exponent to a fraction? Just raise both top and bottom separately: (4/5)^2 = 4^2/5^2 = 16/25, making fractions friendlier. Who knew division could be so straightforward?
  6. Zero Exponent Rule - Any non-zero number to the zero power equals one. Seriously - 7^0, 100^0, or x^0 all collapse to 1, so zero is the ultimate exponent equalizer. Remember: zero on top, one everywhere!
  7. Negative Exponent Rule - Negative exponents flip your base into a reciprocal: a^(-m) = 1/a^m. For example, 2^(-3) = 1/2^3 = 1/8, so negative means "turn it upside down." Zero fear for negatives!
  8. Fractional Exponents - Think of fractional exponents as secret root agents: a^(m/n) = ❿√(a^m). Example: 8^(1/3) = ³√8 = 2, so you can root out answers with ease. Fractions meet radicals in perfect harmony!
  9. Combining Exponent Rules - When you face a combo challenge, tackle one rule at a time and keep track of your steps. For instance, (x^2 × x^3)^4 = x^((2+3)×4) = x^20, mixing product and power rules seamlessly. You're officially an exponent ninja!
  10. Practice Problems - Regular drills reinforce your exponent muscles. Try (2^3 × 2^4) ÷ 2^5 to test multiplication, subtraction, and more all in one problem! Grab a pencil, challenge a friend, and watch your confidence skyrocket.
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