Algebra Indices Study Guide

Algebra Indices Flashcards Study Notes

• a⁹ can be expressed as a⁴ multiplied by a⁵, illustrating the properties of exponents.
• a⁴b² is the product of a³, a, and b², showing the combination of variables with different powers.
• 70a⁴ is derived from multiplying 10a⁷ by 7a⁻³, highlighting the use of negative indices.
• 22ab¹⁵ results from the multiplication of 11ab¹³ and 2ab², demonstrating the addition of exponents with the same base.
• y⁷ equals y⁵ multiplied by y², reinforcing the law of exponents for the same bases.
• 12a⁶y²z³ can be factored into 3a⁵γz² and 4aγz, showcasing the distributive property.
• a²⁰ is obtained by multiplying a¹⁷ by a³, underlining exponent addition.
• 12a⁸ can be broken down into 4a¹⁰ and 3a⁻², showing the manipulation of bases with different exponents.
• 120a¹⁴ arises from the product of 10a⁶ and 12a⁸, reinforcing the laws of multiplication in indices.
• 45b⁹ is derived from the product of 5b⁷ and 9b², exemplifying multiplication with exponents.
• 60ab¹³ is computed from 12ab² multiplied by 5ab¹¹, illustrating exponent addition on like terms.
• 21a⁹ shows how 7a⁵ and 3a⁴ combine through multiplication of exponents.
• The term a can be represented as a⁵ divided by a¹ and a³, illustrating the concept of division in indices.
• 10000a¹⁰ results from multiplying 1000a⁸ by 10a², repeating patterns of multiplication.
• 36a⁶ equals 12a⁴ multiplied by 3a², emphasizing the properties of multiplication.
• 8b² can be factored from 16b³ divided by 2b¹, demonstrating the division of exponents.
• 8a⁴ is derived from dividing 32a⁷ by 4a³, showcasing simplification of terms.
• 9b⁵ derives from dividing 81b⁹ by 9b⁴, exemplifying reduction through division.
• 6a² comes from dividing 12a⁴ by 2a², showing how to simplify powers.
• 5x⁶y²z³ results from dividing 60x¹⁰γ³z⁴ by 12x⁴γz, emphasizing division properties.
• b³a² emerges from dividing b¹⁰a⁴ by b⁷a², highlighting applications of indices in division.
• a⁴b results from dividing a⁸ by a⁴b, demonstrating simplification.
• ½a⁹ comes from dividing 6a¹³ by 12a⁴, illustrating the concept of fraction exponents.
• 9a³ equals 90a⁹ divided by 10a⁶, reinforcing the importance of division.
• 1 can be expressed as x² divided by x², emphasizing the zero exponent principle.
• a⁶ can be represented as (a³)², illustrating the power of a power rule.
• 64a²¹ results from cubing (4a⁷), demonstrating exponent multiplication.
• a⁸b¹² is calculated from (a²b³)⁴, showcasing the distribution of exponents across products.
• a⁵⁴ comes from raising (a⁹) to the sixth power, highlighting the laws of indices.
• 6a²¹ results from cubing (2a⁷), showing multiplication of powers.
• 144a¹⁶ is derived from squaring (12a⁸), emphasizing the squaring rule in exponents.
• a²¹ can be expressed as (a⁷)³, reinforcing multiplication with powers.
• a⁶b¹⁴ is the result of squaring (a³b⁷), showcasing compound exponent rules.
• 16a⁸ results from squaring (4a⁴), demonstrating exponent multiplication.
• a³⁵ comes from raising (a⁷) to the fifth power, illustrating the exponentiation rule.
• 2 equals the sum of two instances of x⁰, which equals 1.
• 8 can be expressed as 8a⁰, illustrating the zero exponent concept.
• 0 results from the equation 3⁰ minus a⁰, emphasizing that any non-zero base raised to the power of zero is 1.
• 6 + a is derived from 8e⁰ minus 2a⁰ plus a, reinforcing the idea of constants and variables in summation.