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Questions and Answers
What is the result of simplifying the expression 2^3 × 2^5?
What is the result of simplifying the expression 2^3 × 2^5?
- 2^6
- 4^6
- 4^8
- 2^8 (correct)
What is the value of 2^(-3)?
What is the value of 2^(-3)?
- 8
- 2
- 1/2
- 1/8 (correct)
What is the result of simplifying the expression 3^2 × 4^3?
What is the result of simplifying the expression 3^2 × 4^3?
- 9 × 12
- 12^5
- 144 × 64
- 9 × 64 (correct)
What is the rule for simplifying expressions with like bases?
What is the rule for simplifying expressions with like bases?
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How do you simplify an expression with negative exponents?
How do you simplify an expression with negative exponents?
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Study Notes
Simplifying Expressions With Like Bases
- When simplifying exponential expressions with like bases, multiply the coefficients and add the exponents.
- Rule:
a^m × a^n = a^(m+n) - Example:
2^3 × 2^5 = 2^(3+5) = 2^8
Negative Exponents
- A negative exponent indicates the reciprocal of the base raised to the positive exponent.
- Rule:
a^(-n) = 1/a^n - Example:
2^(-3) = 1/2^3 = 1/8 - When simplifying expressions with negative exponents, rewrite the expression with positive exponents and then simplify.
Simplifying Expressions With Unlike Bases
- When simplifying exponential expressions with unlike bases, simplify each base separately.
- Rule:
(a^m × b^n) = a^m × b^n(simplify each base separately) - Example:
2^3 × 3^2 = (2 × 2 × 2) × (3 × 3) = 8 × 9 = 72 - When there are multiple unlike bases, simplify each base separately and then multiply the results.
Simplifying Expressions With Like Bases
- To simplify exponential expressions with like bases, multiply the coefficients and add the exponents.
- The rule to remember is:
a^m × a^n = a^(m+n). - For example,
2^3 × 2^5is simplified to2^(3+5) = 2^8.
Negative Exponents
- A negative exponent indicates the reciprocal of the base raised to the positive exponent.
- The rule to remember is:
a^(-n) = 1/a^n. - For example,
2^(-3)is equivalent to1/2^3 = 1/8. - When simplifying expressions with negative exponents, rewrite the expression with positive exponents and then simplify.
Simplifying Expressions With Unlike Bases
- When simplifying exponential expressions with unlike bases, simplify each base separately.
- The rule to remember is:
(a^m × b^n) = a^m × b^n(simplify each base separately). - For example,
2^3 × 3^2is simplified to(2 × 2 × 2) × (3 × 3) = 8 × 9 = 72. - When there are multiple unlike bases, simplify each base separately and then multiply the results.
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Description
Learn how to simplify exponential expressions with like bases and negative exponents, including rules and examples.
