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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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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

Simplify x2⋅x5⋅xx^2\cdot x^5\cdot x

Please select an answer first.

Correct answer: A

The correct answer is x8x^8.

  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: Add the exponents of the same base: 2 + 5 + 1 = 8.
  3. Check equivalent form: The correct choice is x8x^8.

Add the exponents of the same base: 2 + 5 + 1 = 8.

2. QuestionMultiple choice

Simplify y9y2\frac{y^9}{y^2}

Please select an answer first.

Correct answer: B

The correct answer is y7y^7.

  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: Subtract the denominator exponent from the numerator exponent: 9 - 2 = 7.
  3. Check equivalent form: The correct choice is y7y^7.

Subtract the denominator exponent from the numerator exponent: 9 - 2 = 7.

3. QuestionMultiple choice

Simplify (a3b2)(a2b4)(a^3b^2)(a^2b^4)

Please select an answer first.

Correct answer: C

The correct answer is a5b6a^5b^6.

  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: Add exponents for each matching base: a has exponent 3 + 2 and b has exponent 2 + 4.
  3. Check equivalent form: The correct choice is a5b6a^5b^6.

Add exponents for each matching base: a has exponent 3 + 2 and b has exponent 2 + 4.

4. QuestionMultiple choice

Simplify (2x2)2(2x^2)^2

Please select an answer first.

Correct answer: D

The correct answer is 4x44x^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: Square both factors: 2 squared is 4 and (x squared) squared is x to the fourth.
  3. Check equivalent form: The correct choice is 4x44x^4.

Square both factors: 2 squared is 4 and (x squared) squared is x to the fourth.

5. QuestionMultiple choice

Which expression is already written as a quotient of powers?

Please select an answer first.

Correct answer: A

The correct answer is p4q2\frac{p^4}{q^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 expression p to the fourth divided by q squared is a quotient of powers.
  3. Check equivalent form: The correct choice is p4q2\frac{p^4}{q^2}.

The expression p to the fourth divided by q squared is a quotient of powers.

6. QuestionMultiple choice

Simplify x5x−2\frac{x^5}{x^{-2}}

Please select an answer first.

Correct answer: B

The correct answer is x7x^7.

  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: Subtract exponents: 5 - (-2) = 7.
  3. Check equivalent form: The correct choice is x7x^7.

Subtract exponents: 5 - (-2) = 7.

7. QuestionMultiple choice

Simplify 32⋅343^2\cdot3^4

Please select an answer first.

Correct answer: C

The correct answer is 363^6.

  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: 2 + 4 = 6.
  3. Check equivalent form: The correct choice is 363^6.

The bases match, so add exponents: 2 + 4 = 6.

8. QuestionMultiple choice

Evaluate m0+n0m^0+n^0 for nonzero m and n.

Please select an answer first.

Correct answer: D

The correct answer is 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: Each nonzero term raised to the zero power equals 1, so the sum is 1 + 1 = 2.
  3. Check equivalent form: The correct choice is 2.

Each nonzero term raised to the zero power equals 1, so the sum is 1 + 1 = 2.

9. QuestionMultiple choice

Evaluate 2−32^{-3}

Please select an answer first.

Correct answer: A

The correct answer is 18\frac{1}{8}.

  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: A negative exponent gives a reciprocal: 2 to the negative 3 equals 1/2 cubed = 1/8.
  3. Check equivalent form: The correct choice is 18\frac{1}{8}.

A negative exponent gives a reciprocal: 2 to the negative 3 equals 1/2 cubed = 1/8.

10. QuestionMultiple choice

Simplify (x2)3x4\frac{(x^2)^3}{x^4}

Please select an answer first.

Correct answer: B

The correct answer is x2x^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: First multiply exponents to get x to the sixth, then subtract 4 to get x squared.
  3. Check equivalent form: The correct choice is x2x^2.

First multiply exponents to get x to the sixth, then subtract 4 to get x squared.

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