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Exponents and Polynomials

A free Algebra I lesson from the “Exponents and Polynomials” unit, with a worked example and practice problems including step-by-step solutions.

Exponent rules help simplify repeated multiplication. Polynomials are expressions made of terms with whole-number exponents. Like terms can be combined across polynomials. In Exponents and Polynomials, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.

What you'll learn

Why it matters: Exponents and polynomials show up in area formulas, compact growth patterns, and expressions that describe repeated structure.

Worked example

Problem. Simplify x^3 times x^4.

  1. The bases are the same.
  2. When multiplying powers with the same base, add exponents.
  3. 3 + 4 = 7, so the result is x^7.
  4. Connect the result back to Exponents and Polynomials so the method and meaning are both clear.

Answer: x^7

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Simplify x^2 times x^5.

Show solution
  1. Same base means add exponents.
  2. 2 + 5 = 7.

Answer: x^7

2. Simplify a^6 divided by a^2.

Show solution
  1. Same base division means subtract exponents.
  2. 6 - 2 = 4.

Answer: a^4

3. How many terms are in 3x^2 + 5x - 8?

Choices: 1 · 2 · 3 · 4

Show solution
  1. Terms are separated by plus or minus signs.
  2. There are 3 terms.

Answer: 3

4. Simplify (2x + 5) + (3x - 1).

Show solution
  1. Combine x terms: 2x + 3x = 5x.
  2. Combine constants: 5 - 1 = 4.

Answer: 5x + 4

5. Simplify (7x - 4) - (2x + 3).

Show solution
  1. Distribute the subtraction: 7x - 4 - 2x - 3.
  2. Combine to get 5x - 7.

Answer: 5x - 7

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