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Quizzes > Mathematics

Exponents Quiz: Grade 8 Word Problems and Powers Practice

Quick, 20-question exponents test. Instant results.

Editorial: Review CompletedCreated By: Maynard AlhambraUpdated Aug 28, 2025
Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Exponent Extravaganza, a high school math quiz.

Use this exponents quiz to practice Grade 8 word problems, powers, and exponential expressions. Work through 20 real-world questions with instant results to see what you know and what to review. For targeted practice, try the exponent rules quiz, or extend your skills with the exponents practice quiz.

What is 2^3?
9
12
6
8
2^3 means 2 multiplied by itself three times: 2 * 2 * 2 = 8. Therefore, option A is correct.
What is the value of 10^0?
0
1
10
Undefined
Any nonzero number raised to the power of zero is equal to 1. Thus, 10^0 equals 1.
What is the result of 3^2 * 3^3?
3^4
243
9
3^6
When multiplying powers with the same base, add the exponents: 3^2 * 3^3 = 3^(2+3) = 3^5, which equals 243.
What is the value of (2 * 3)^2?
36
10
12
5
Using the power of a product rule, (2 * 3)^2 equals 2^2 * 3^2 = 4 * 9 = 36. So, the correct answer is 36.
What is the value of 5^-1?
5
1
-5
1/5
A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. Therefore, 5^-1 equals 1/5.
Simplify the expression (x^3)^2.
2x^3
x^5
x^9
x^6
When raising a power to another power, multiply the exponents: (x^3)^2 = x^(3*2) = x^6. Thus, the correct answer is x^6.
Simplify 2^3 * 4^2.
32
256
128
64
Rewrite 4^2 as (2^2)^2 = 2^4, then 2^3 * 2^4 = 2^(3+4) = 2^7, which equals 128. Therefore, 128 is correct.
What is 10^5 / 10^2 equal to?
10^7
10^2
10^5
10^3
Using the quotient of powers rule, subtract the exponents: 10^5 / 10^2 = 10^(5-2) = 10^3, which is 1000.
Evaluate (3^2 * 3^3) / 3^4.
81
3
27
9
First, 3^2 * 3^3 equals 3^(2+3) = 3^5. Then, dividing by 3^4 gives 3^(5-4) = 3. Hence, the correct answer is 3.
What is the simplified form of (2x)^3?
8x^3
2^3 + x^3
2x^6
6x^3
Using the power of a product rule, (2x)^3 is equal to 2^3 * x^3, which calculates to 8x^3. Thus, 8x^3 is correct.
Express 16^(3/4) in simplest form.
8
4
16
64
Rewrite 16 as 2^4 so that 16^(3/4) becomes (2^4)^(3/4) = 2^(4*(3/4)) = 2^3, which is 8. Therefore, 8 is the correct answer.
Simplify x^0 + y^0.
2
0
1
Undefined
Any nonzero number raised to the power of zero equals 1. Thus, x^0 + y^0 equals 1 + 1, which is 2.
Solve for x: 2^(x+1) = 2^5.
5
3
6
4
Since the bases are the same, the exponents must be equal. Setting x + 1 = 5 gives x = 4.
Simplify 5^-2 * 5^4.
5^-2
5^2
5^6
5^-6
Multiplying powers with the same base means adding the exponents: -2 + 4 = 2. Therefore, the expression simplifies to 5^2, which is 25.
Express √(x^5) using rational exponents.
x^(2/5)
x^(5/2)
x^2
x^5
Taking the square root is equivalent to raising to the 1/2 power. Therefore, √(x^5) = (x^5)^(1/2) = x^(5/2).
Simplify the expression ((2^-3 * 4^2) / 8).
1/2
1/4
4
2
Convert all terms to base 2: 2^-3 remains as is and 4^2 becomes (2^2)^2 = 2^4, so 2^-3 * 2^4 = 2^(1). Dividing by 8 (which is 2^3) gives 2^(1-3) = 2^-2 = 1/4.
Solve for n in the equation 3^(2n-1) = 3^5.
6
4
3
2
Since the bases are identical, set the exponents equal: 2n - 1 = 5. Solving this gives 2n = 6, so n = 3.
If a^m = b and a^n = c, what is a^(m+n) equal to in terms of b and c?
b/c
bc
c - b
b + c
The rule for multiplying powers with the same base states that a^(m+n) = a^m * a^n. Since a^m = b and a^n = c, the product is bc.
Simplify ((x^(1/2))^4) / x^2.
x
1
x^2
0
Raising x^(1/2) to the 4th power gives x^(4*(1/2)) = x^2. Dividing x^2 by x^2 results in 1, provided x is nonzero.
Simplify (27x^9)^(2/3).
27x^6
3x^6
9x^6
9x^3
Express 27 as 3^3 so that 27^(2/3) = (3^3)^(2/3) = 3^2 = 9, and (x^9)^(2/3) = x^(9*(2/3)) = x^6. Therefore, the simplified form is 9x^6.
0
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Study Outcomes

  1. Apply exponent rules to simplify algebraic expressions.
  2. Analyze and convert between exponential forms.
  3. Solve problems involving the multiplication and division of exponential expressions.
  4. Evaluate expressions containing powers using the properties of exponents.
  5. Identify common misconceptions and correct errors in exponent manipulation.

Exponents Quiz & Test: Word Problems Review Cheat Sheet

  1. Master the Product Rule - When multiplying like bases, add the exponents to simplify expressions. For example, 3² × 3³ becomes 3^(2+3) = 3❵, so no more tedious expansions. Using this rule, you can combine powers in a flash!
  2. Understand the Quotient Rule - To divide like bases, subtract the exponents and watch your workload shrink. For instance, 5❷ ÷ 5³ = 5^(7−3) = 5❴, avoiding gigantic calculations. Keep this rule handy for any division puzzle!
  3. Apply the Power of a Power Rule - When raising an exponentiated term to another power, multiply the exponents to stay neat. For example, (2³)❴ = 2^(3×4) = 2¹², giving you a shortcut to big results. This rule is a multiplier-level hack you'll love!
  4. Use the Power of a Product Rule - Distribute the exponent across each factor in a product for easy simplification. For example, (2×3)❴ = 2❴ × 3❴ makes computation a breeze and keeps work tidy. Applying this rule saves time on every multivariable exponent problem!
  5. Remember the Zero Exponent Rule - Any non-zero number raised to zero equals one, giving you a guaranteed result. For instance, 7❰ = 1, so you never hit a dead end when simplifying expressions. This simple rule is a lifesaver in algebraic clean‑up!
  6. Handle Negative Exponents - A negative exponent flips your base into the denominator as a positive power. For example, 2❻³ = 1/2³ = 1/8, turning confusing negatives into neat fractions. Master this rule to keep fractions under control!
  7. Simplify with the Power of a Quotient Rule - Distribute an exponent to both numerator and denominator: (a/b)❿ = a❿/b❿. For example, (2/3)² = 2²/3² = 4/9, making fraction exponents straightforward. This rule ensures no messy surprises in division problems!
  8. Convert Fractional Exponents to Radicals - A fractional exponent's denominator tells you which root to take: a^(m/n) = √[n]{aᵝ}. For example, 8^(2/3) = √[3]{8²} = √[3] = 4, turning powers into roots instantly. Use this rule to switch between radicals and exponents with confidence!
  9. Practice the First Power Rule - Raising any number to the first power leaves it unchanged, so a¹ = a every time. For instance, 9¹ = 9, which helps you spot simple simplifications in algebra. Keep this rule in mind to avoid extra steps!
  10. Engage with Interactive Quizzes - Test your exponent skills with fun, interactive quizzes to reinforce learning and build confidence. Quizzing yourself is a proven way to solidify tricky rules and spot any weak spots. Dive in and master exponents like a pro!
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