Integer Exponents

Learn and apply integer exponents using equations, examples, and interpretation.

Lesson 1 of 53 parts Practice Flashcards

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Product of Powers

Objective: Explain and use product of powers in an Algebra 1 problem.

For a nonzero base x, x^m·x^n=x^(m+n); the rule requires the same base. No, not by this rule.

Worked examples

Try itExample 1.1: Simplify x^4 · x^5 as x^n. Find n.Show answer

9. For the same base, add the exponents. The answer is 9.

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Objective: Explain and use product of powers in an Algebra 1 problem.

For a nonzero base x, x^m·x^n=x^(m+n); the rule requires the same base. No, not by this rule.

Worked examples

Try itExample 1.1: Simplify x^4 · x^5 as x^n. Find n.Show answer

9. For the same base, add the exponents. The answer is 9.

Objective: Explain and use quotient and zero exponents in an Algebra 1 problem.

For x≠0, x^m/x^n=x^(m−n) and x^0=1; restrictions prevent division by zero. Division by zero is undefined.

Worked examples

Try itExample 2.1: Simplify x^10/x^2 as x^n, for x≠0. Find n.Show answer

8. For the same nonzero base, subtract denominator exponent. The answer is 8.

Objective: Explain and use negative exponents in an Algebra 1 problem.

For nonzero x, x^(−n)=1/x^n; a negative exponent does not make the entire value necessarily negative. No, it equals one eighth.

Worked examples

Try itExample 3.1: Evaluate 3^11 for integer exponent 11.Show answer

177147. Multiply the base by itself the stated number of times. The answer is 177147.

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