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Quizzes > High School Quizzes > Mathematics

Grade 8 Exponents Practice Quiz PDF

Practice free answer worksheets for exponents, science & more

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting the Exponent Power-Up Quiz for middle school students.

What is 2^3?
6
9
8
5
2^3 means multiplying 2 by itself 3 times (2 * 2 * 2), which equals 8. This is a basic definition of exponents.
What is the value of 5^0 (given 5 is not zero)?
1
5
0
Undefined
Any nonzero number raised to the power of 0 is equal to 1. This is one of the fundamental properties of exponents.
Which exponent rule is used when multiplying two expressions with the same base?
Product Rule
Power of a Power Rule
Quotient Rule
Zero Exponent Rule
When multiplying terms with the same base, you add the exponents. This is known as the Product of Powers Rule.
What does (3^2)^3 simplify to?
3^9
3^6
3^5
3^8
Using the power of a power rule, (3^2)^3 becomes 3^(2*3), which simplifies to 3^6. This rule multiplies the exponents.
Which expression correctly represents the division rule for exponents with the same base?
a^m / a^n = a^(mn)
a^m / a^n = a^(m-n)
a^m / a^n = a^(n-m)
a^m / a^n = a^(m+n)
When dividing exponents with the same base, you subtract the exponent in the denominator from the exponent in the numerator. This is the Quotient Rule.
Simplify the expression: 2^3 * 2^4.
64
512
16
128
When multiplying exponents with the same base, you add the exponents: 2^(3+4) equals 2^7, which is 128. This is a direct application of the Product of Powers Rule.
Simplify the expression: 3^4 / 3^2.
6
12
1
9
Using the Quotient Rule, subtract the exponent in the denominator from the exponent in the numerator: 3^(4-2)=3^2, which equals 9. This shows how exponent subtraction simplifies division.
Express 4^-2 in its simplest form.
1/16
4^2
16
1/8
A negative exponent means taking the reciprocal of the base raised to the positive exponent. Thus, 4^-2 is the same as 1/4^2, which equals 1/16.
Simplify the expression: (x^3)^2.
x^9
x^6
x^5
2x^3
Applying the power of a power rule, (x^3)^2 becomes x^(3*2), which simplifies to x^6. This involves multiplying the exponents.
Simplify the expression: (2 * 3)^3.
216
729
512
64
The exponent applies to both factors: (2 * 3)^3 becomes 2^3 * 3^3. Multiplying these results, 8 * 27, gives 216.
Simplify the expression: 16^(3/4).
2
16
4
8
Determine the fourth root of 16, which is 2, and then raise it to the 3rd power: 2^3 equals 8. This problem uses the concept of fractional exponents.
Simplify the expression: (a^5 * b^3) / (a^2 * b).
a^7b^4
a^3b
a^2b^3
a^3b^2
Subtract the exponents of like bases: for a, 5 - 2 equals 3; for b, 3 - 1 equals 2, giving a^3b^2. This is a straightforward use of the Quotient Rule.
Simplify the expression: 9^(1/2).
81
3
4.5
9
A fractional exponent of 1/2 denotes the square root. Since the square root of 9 is 3, the expression simplifies to 3.
What is the value of (-2)^3?
8
4
-8
0
Multiplying -2 by itself three times gives (-2) * (-2) * (-2) which results in -8. An odd exponent preserves the sign of a negative base.
Simplify the expression: (2^3)^2 / 2^4.
8
2
16
4
First, apply the power of a power rule: (2^3)^2 becomes 2^6. Then, divide by 2^4, subtracting the exponents to get 2^(6-4) which equals 2^2, or 4.
Simplify the expression: a^(2x) * a^(3) / a^(x+4).
a^(x-2)
a^(2x-1)
a^(x-1)
a^(x+1)
Combine the exponents in the numerator using the Product Rule to get a^(2x+3), then apply the Quotient Rule by subtracting (x+4). The result is a^(x-1).
Simplify the expression: 27^(2/3).
6
27
81
9
Take the cube root of 27, which is 3, and then square the result: 3^2 equals 9. This shows the use of fractional exponents to denote roots and powers.
If 2^x = 32, what is the value of x?
10
6
4
5
Recognize that 32 is a power of 2, specifically 2^5. By equating the exponents, we determine that x = 5.
Simplify the expression: (x^2)^3 * x^-4.
x^6
x^8
x^2
x^4
Apply the power of a power rule to obtain x^(2*3) = x^6, and then combine with x^-4 using the product rule: x^(6-4) simplifies to x^2. This problem combines multiple exponent rules.
Simplify the expression: (4x^3)^2 / (2x)^3.
2x^3
8x^3
4x^6
2x^2
Expand the terms: (4x^3)^2 becomes 16x^6 and (2x)^3 becomes 8x^3. Dividing these gives (16/8) * x^(6-3) = 2x^3. This requires careful application of both distribution of exponents and the quotient rule.
0
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Study Outcomes

  1. Apply exponent rules to simplify expressions.
  2. Analyze operations involving positive, negative, and zero exponents.
  3. Solve problems by correctly manipulating exponent properties.
  4. Evaluate complex expressions using multiple exponent operations.
  5. Validate results by cross-checking different approaches to exponent simplification.

Grade 8 Exponents Worksheets w/ Answers Cheat Sheet

  1. Product Rule - When you multiply two exponents with the same base, simply add the exponents to combine them into one powerful exponent. It's like stacking identical building blocks - 23 × 24 becomes 27. Product Rule on Symbolab
  2. Quotient Rule - When dividing expressions with the same base, subtract the exponent in the denominator from the exponent in the numerator. Think of it as undoing part of the power - 57 ÷ 53 = 54. This rule turns big fractions into simple powers. Quotient Rule on Symbolab
  3. Power of a Power Rule - To raise a power to another power, multiply the exponents for extra turbo charge. It's like stacking power-ups in a video game - (32)4 = 38. Power of a Power on GreeneMath
  4. Power of a Product Rule - Distribute the exponent to each factor inside parentheses so everyone shares the power. For example, (2×3)4 becomes 24×34, splitting the work evenly. Power of a Product at ByteLearn
  5. Power of a Quotient Rule - Apply the exponent separately to both numerator and denominator. Picture spreading frosting equally on two cupcakes - (2/3)3 = 23/33. Power of a Quotient on Symbolab
  6. Zero Exponent Rule - Any non-zero base raised to the zero power equals one, because you've taken away all of its multiplying power. Remember, a0 = 1, so 70 = 1. Zero Exponent Lesson on GreeneMath
  7. Negative Exponent Rule - A negative exponent flips your base into the denominator as a positive power. It's like stepping downstairs instead of climbing - 2−3 = 1/23 = 1/8. Negative Exponents at ByteLearn
  8. Fractional Exponents - Fractional exponents link exponents to roots: the denominator tells you which root to take, the numerator how many times to raise. For example, 82/3 = (³√8)2 = 4. Fractional Exponents Guide
  9. Multiplying Different Bases with the Same Exponent - When different bases share an exponent, multiply the bases first then raise the result to that exponent. So 23×33 = 63. Multiplying Bases at Symbolab
  10. Dividing Different Bases with the Same Exponent - If different bases share the same exponent, divide the bases and then apply the exponent to the quotient. For instance, 42÷22 = 22 = 4. Dividing Bases at Symbolab
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