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Exponents and Polynomials Practice Tests

These Grade 9 Math practice tests cover positive, zero, and negative exponents, products and quotients of powers, powers of powers, scientific notation, monomials, polynomial degree and coefficients, polynomial addition and subtraction, multiplication, factoring, and algebraic models.

Skills covered

  • Applying product, quotient, power, and negative-exponent rules
  • Evaluating powers and rewriting expressions with positive exponents
  • Identifying degree, leading coefficient, constant term, and like terms
  • Adding, subtracting, multiplying, and factoring polynomials
  • Using polynomial expressions for area, volume, functions, sequences, and scientific notation

How to use these practice tests

Identify matching bases before applying exponent rules, combine only like terms, distribute to every term, and check polynomial products by substituting a simple value when needed.

For more Grade 9 Math practice, return to the Grade 9 Math category.

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5. Test

Grade 9 Exponents and Polynomials Practice Tests

Practice Grade 9 Math questions about exponent rules, zero and negative exponents, monomials, polynomial degree, polynomial operations, factoring, and algebraic models.

Choose the best answer. Apply exponent rules, combine like terms, distribute carefully, write polynomials in standard form, and check equivalent expressions.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

A square has side length 3x3x. What is its area?

Please select an answer first.

Correct answer: A

The correct answer is 9x29x^2.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: The area is side squared: (3x) squared = 9x squared.
  3. Check equivalent form: The correct choice is 9x29x^2.

The area is side squared: (3x) squared = 9x squared.

2. QuestionMultiple choice

A rectangle has dimensions x+2x+2 and x+5x+5. What is its area?

Please select an answer first.

Correct answer: B

The correct answer is x2+7x+10x^2+7x+10.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: Multiply (x + 2)(x + 5) to get x squared + 7x + 10.
  3. Check equivalent form: The correct choice is x2+7x+10x^2+7x+10.

Multiply (x + 2)(x + 5) to get x squared + 7x + 10.

3. QuestionMultiple choice

A cube has side length 2x2x. What is its volume?

Please select an answer first.

Correct answer: C

The correct answer is 8x38x^3.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: Volume is side cubed: (2x) cubed = 8x cubed.
  3. Check equivalent form: The correct choice is 8x38x^3.

Volume is side cubed: (2x) cubed = 8x cubed.

4. QuestionMultiple choice

Write 4.2 × 10 to the third power in standard form.

Please select an answer first.

Correct answer: D

The correct answer is 4,200.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: Multiplying by 10 cubed moves the decimal three places to the right: 4,200.
  3. Check equivalent form: The correct choice is 4,200.

Multiplying by 10 cubed moves the decimal three places to the right: 4,200.

5. QuestionMultiple choice

Simplify 103⋅10210^3\cdot10^2

Please select an answer first.

Correct answer: A

The correct answer is 10510^5.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: The bases match, so add exponents: 3 + 2 = 5.
  3. Check equivalent form: The correct choice is 10510^5.

The bases match, so add exponents: 3 + 2 = 5.

6. QuestionMultiple choice

If f(x)=x2+2xf(x)=x^2+2x, what is f(3)f(3)?

Please select an answer first.

Correct answer: B

The correct answer is 15.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: Substitute 3: 3 squared + 2(3) = 9 + 6 = 15.
  3. Check equivalent form: The correct choice is 15.

Substitute 3: 3 squared + 2(3) = 9 + 6 = 15.

7. QuestionMultiple choice

If 2x=162^x=16

Please select an answer first.

Correct answer: C

The correct answer is x = 4.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: Since 16 = 2 to the fourth power, x = 4.
  3. Check equivalent form: The correct choice is x = 4.

Since 16 = 2 to the fourth power, x = 4.

8. QuestionMultiple choice

Which comparison is true?

Please select an answer first.

Correct answer: D

The correct answer is 32>233^2>2^3.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: 3 squared is 9 and 2 cubed is 8, so 9 > 8.
  3. Check equivalent form: The correct choice is 32>233^2>2^3.

3 squared is 9 and 2 cubed is 8, so 9 > 8.

9. QuestionMultiple choice

Which expression is equivalent to x2+x2x^2+x^2?

Please select an answer first.

Correct answer: A

The correct answer is 2x22x^2.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: The terms are like terms, so add their coefficients: 1x squared + 1x squared = 2x squared.
  3. Check equivalent form: The correct choice is 2x22x^2.

The terms are like terms, so add their coefficients: 1x squared + 1x squared = 2x squared.

10. QuestionMultiple choice

Which expression is equivalent to (x+1)2(x+1)^2?

Please select an answer first.

Correct answer: B

The correct answer is x2+2x+1x^2+2x+1.

  1. Identify the exponent or polynomial structure: Determine which exponent rule, polynomial operation, degree, coefficient, or model is being used.
  2. Apply the rule carefully: Use the square pattern: x squared + 2x + 1.
  3. Check equivalent form: The correct choice is x2+2x+1x^2+2x+1.

Use the square pattern: x squared + 2x + 1.

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