Algebra Exponent Laws Flashcards

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.