Questions and Answers
What does the expression x²⁴ represent?
What does the expression a⁸b¹² simplify to?
a to the power of 8 times b to the power of 12
What is represented by the term 2c⁷?
2 times c to the power of 7
What does the expression 15x⁸ represent?
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What is the definition of x⁷y⁷?
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What does the expression 9x² simplify to?
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What does a⁴ represent?
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What is represented by a²¹b⁶?
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What does 4c⁵ represent?
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What is x¹¹?
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What does the expression x²⁰ simplify to?
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What does a⁸ represent?
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What does a¹⁸b⁶ represent?
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What does the expression 3u²⋅8u⁶ simplify to?
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What is the result of (−3d)(5d⁵)(−d³)?
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What does (10x⁸y⁵) / (-2xy²) simplify to?
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What does (24a²b) / (6ab) simplify to?
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What is (x²)(x³)?
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What does 5x⁴/x² simplify to?
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What is the result of (7x²)(x³)?
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What does (3x⁴)⁵ equal?
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What is (-7x²)(4x⁴)?
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What is x⁸ ÷ x⁵?
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What does (-2x³y²)(5xy⁴) simplify to?
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What does (6h)⁴ represent?
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What is (-2x³y²)(5xy⁴)?
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What is 3⁸?
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What does (3³)⁵ equal?
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What does (4⁷)² simplify to?
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What is 4⁴?
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What does 5¹⁰ represent?
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Study Notes
Exponential Expressions
- x²⁴ represents a variable x raised to the power of 24.
- a⁸b¹² defines two variables, a raised to the power of 8 and b raised to the power of 12.
- 2c⁷ indicates a coefficient of 2 multiplied by the variable c raised to the power of 7.
- 15x⁸ shows a coefficient of 15 multiplied by the variable x raised to the power of 8.
- x⁷y⁷ indicates the product of two variables, x and y, each raised to the power of 7.
- 9x² signifies a coefficient of 9 multiplied by x raised to the power of 2.
- a⁴ is a single variable a raised to the power of 4.
- a²¹b⁶ denotes a raised to the power of 21 multiplied by b raised to the power of 6.
- 4c⁵ consists of a coefficient of 4 and c raised to the power of 5.
- x¹¹ indicates x raised to the power of 11 and operates independently.
- x²⁰ represents x raised to the power of 20, a higher exponent than earlier examples.
- a⁸ is simply a raised to the power of 8, without other variables.
- a¹⁸b⁶ shows a raised to the power of 18 multiplied by b raised to the power of 6.
Simplifying Products and Quotients
- For the product (3u²)(8u⁶), the simplified result is 24u⁸; combine coefficients and add exponents.
- The multiplication of (−3d)(5d⁵)(−d³) results in 15d⁹; negative coefficients multiplied yield a positive result.
- Dividing (10x⁸y⁵) by (−2xy²) simplifies to -5x⁷y³; adjust the signs and reduce the variables.
- The expression (24a²b) divided by (6ab) simplifies to 4a; reduce coefficients and variables.
Laws of Exponents
- The multiplication of powers law (x²)(x³) results in x⁵; add the exponents.
- Simplifying 5x⁴/x² yields 5x²; subtract the exponents for the same base.
- The product (7x²)(x³) simplifies to 7x⁵; again, add exponents.
- Raising a power to a power (3x⁴)⁵ results in 3⁵x²⁰; multiply the exponent.
Negative Coefficients
- The expression (-7x²)(4x⁴) simplifies to -28x⁶; multiply coefficients and add exponents.
- The division x⁸ ÷ x⁵ results in x³; apply the same rules of exponent subtraction.
- The product (-2x³y²)(5xy⁴) simplifies to -10x⁴y⁶; multiply coefficients and add the exponents of like variables.
Further Simplification
- (6h)⁴ simplifies to 6⁴h⁴; distribute the exponent.
- 3⁸ breaks down into (3⁵)(3³) by adding exponents.
- (3³)⁵ results in 3¹⁵; another demonstration of power to a power.
- The expression (4⁷)² simplifies to 4¹⁴; distribute the exponent.
- 4⁴ can be expressed as 4⁶ / 4², showing the quotient of powers.
- 5¹⁰ can also be represented as (5²)⁵, reinforcing the power of a power concept.
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Test your knowledge of simplifying algebraic expressions with exponents using these flashcards. Each card features a term composed of variables and exponents, allowing you to review important exponent rules. Perfect for mastering the laws of exponents in algebra.
