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Quizzes > High School Quizzes > Mathematics

Laws of Exponents Practice Quiz

Boost exponent skills with an interactive practice test

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art illustrating a trivia quiz on exponent rules for high school math students.

Simplify: x^3 * x^2.
2x^5
x^5
x^6
x^9
When multiplying exponential expressions with the same base, add their exponents (3 + 2 = 5). The other options involve incorrect operations.
Simplify: (a^2)^3.
a^5
a^9
a^8
a^6
Raising a power to another power multiplies the exponents, so (a^2)^3 = a^(2*3) = a^6. The other choices are results of common mistakes.
What is the value of 5^0?
 
5
0
1
Any nonzero number raised to the power of 0 is 1. The other options reflect common misconceptions regarding the zero exponent.
Simplify: 3^4 / 3^2.
3^8
3^1
3^6
3^2
Divide by subtracting exponents: 3^(4-2) = 3^2. The other options come from misapplications of the exponent rules.
Simplify: (2^3 * 2^2) / 2^4.
2^9
2^3
2^5
2^1
Combine the exponents in the numerator by addition (3 + 2 = 5) and then subtract the exponent in the denominator (5 - 4 = 1), yielding 2^1. The other options involve incorrect operations.
Simplify: (x^5)^2.
2x^5
x^10
x^12
x^7
When raising a power to a power, multiply the exponents: 5*2 = 10, so the expression simplifies to x^10. The other answers result from common errors.
Simplify: y^3 * y^-1.
y^2
y^-4
y^0
y^4
Add the exponents: 3 + (-1) equals 2, yielding y^2. The other options are the result of errors in exponent arithmetic.
Simplify: 2^3 * 2^-5.
2^8
2^-8
2^2
2^-2
When multiplying with the same base, add the exponents: 3 + (-5) = -2, so the expression is 2^-2. The other options are from miscalculating the sum.
Simplify: (3^2)^3.
3^6
3^9
3^8
3^5
Multiply the exponents: 2 multiplied by 3 equals 6, so the expression simplifies to 3^6. The other choices represent miscalculations in exponent multiplication.
Evaluate: 16^(3/4).
64
4
16
8
Express 16 as 2^4, so 16^(3/4) becomes (2^4)^(3/4) = 2^3 = 8. The other answers do not correctly apply the fractional exponent rule.
Simplify: (a^-3)^2.
a^6
-a^6
a^-6
a^-5
Multiply the exponent -3 by 2 to get -6, so the expression simplifies to a^-6. The other options arise from neglecting the negative sign or miscomputing the multiplication.
Simplify: (b^2)^3 * b^-4.
b^2
b^4
b^-6
b^6
First, (b^2)^3 equals b^6 by multiplying the exponents, then b^6 multiplied by b^-4 gives b^(6-4) = b^2. The other options reflect errors in combining the exponents.
Simplify: (8x^3)^(2/3).
8x^2
4x^3
4x^2
2x^2
Take the cube root of 8 to get 2 and then raise it to the power of 2 to obtain 4. Simultaneously, (x^3)^(2/3) becomes x^2, resulting in 4x^2. The other options come from errors in handling the fractional exponent.
Simplify: (z^5 / z^2)^2.
z^6
z^3
z^10
z^7
Subtract the exponents in the fraction to get z^(5-2) = z^3, then raise it to the power of 2: (z^3)^2 = z^6. The other options misapply the exponent rules.
Simplify: (10^-2 * 10^5) / 10^3.
10^2
10^3
10
1
Combine the exponents by adding and subtracting: (-2 + 5 - 3) equals 0, so the expression becomes 10^0 which is 1. The other options reflect mistakes in exponent arithmetic.
Solve for x: (2^(3x))^2 = 2^(12).
6
4
2
12
Simplify the left side by multiplying the exponents: (2^(3x))^2 becomes 2^(6x). Equate 6x = 12 and solve for x to get x = 2. The other answers do not satisfy this equation.
Simplify: [(5^3)^2 * 5^-4] / 5^2.
5
1
125
25
First, (5^3)^2 equals 5^6. Multiplying by 5^-4 gives 5^(6-4) = 5^2, which divided by 5^2 becomes 5^(2-2) = 5^0 = 1. The alternatives are incorrect applications of exponent rules.
If 2^(x+1) = 16, what is the value of x?
4
1
3
2
Recognize that 16 equals 2^4. Equate the exponents: x + 1 = 4, which yields x = 3. The other options result from misequating the exponents.
Simplify: (27y^6)^(1/3) / y^2.
27
y^2
3
9
Take the cube root of 27 to get 3 and of y^6 to get y^2; then, (27y^6)^(1/3) becomes 3y^2, which divided by y^2 simplifies to 3. The other options do not correctly apply the rules.
Simplify: (a^2 * b^-3)^3.
a^6 * b^9
a^6 / b^9
a^3 / b^3
a^5 / b^8
Apply the power to each factor: (a^2)^3 becomes a^6 and (b^-3)^3 becomes b^-9, resulting in a^6/b^9. The other options result from misapplying exponent multiplication.
0
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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. Mometrix Academy: Laws of 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! Mometrix Academy: Laws of Exponents
  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! Mometrix Academy: Laws of Exponents
  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! Mometrix Academy: Laws of Exponents
  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? Mometrix Academy: Laws of Exponents
  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! Mometrix Academy: Laws of Exponents
  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! Mometrix Academy: Laws of Exponents
  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! Third Space Learning: Laws of Exponents
  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! Mometrix Academy: Laws of Exponents
  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. Teachoo: Exponent Practice Questions
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