Algebra Indices Study Guide

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Questions and Answers

What is the equivalent of a⁹?

a⁴ x a⁵

What is the expanded form of a⁴b²?

a³ x a x b²

What does 70a⁴ represent?

10a⁷ x 7a⁻³

How can 22ab¹⁵ be expressed?

11ab¹³ x 2ab² Signup and view all the answers

What is y⁷ equivalent to?

y⁵ x y² Signup and view all the answers

What does 12a⁶y²z³ equal?

3a⁵y²z² x 4aγz Signup and view all the answers

What is a²⁰ equivalent to?

a¹⁷ x a³ Signup and view all the answers

What does 12a⁸ equal?

4a¹⁰ x 3a⁻² Signup and view all the answers

What is 120a¹⁴ equal to?

10a⁶ x 12a⁸ Signup and view all the answers

How can 45b⁹ be expressed?

5b⁷ x 9b² Signup and view all the answers

What does 60ab¹³ equal?

12ab² x 5ab¹¹ Signup and view all the answers

What is 21a⁹ equivalent to?

7a⁵ x 3a⁴ Signup and view all the answers

What does a equal when simplified?

a⁵ ÷ a¹ ÷ a³ Signup and view all the answers

What is the equivalent of 10000a¹⁰?

1000a⁸ x 10a² Signup and view all the answers

What does 36a⁶ equal?

12a⁴ x 3a² Signup and view all the answers

What is 8b² equal to?

16b³ ÷ 2b₁ Signup and view all the answers

What is 8a⁴ equivalent to?

32a⁷ ÷ 4a³ Signup and view all the answers

How can 9b⁵ be expressed?

81b⁹ ÷ 9b⁴ Signup and view all the answers

What is the equivalent of 6a²?

12a⁴ ÷ 2a² Signup and view all the answers

What does 5x⁶y²z³ equal?

60x¹⁰γ³z⁴ ÷ 12x⁴γz Signup and view all the answers

What is b³a² equal to?

b¹⁰a⁴ ÷ b⁷a² Signup and view all the answers

What is a⁴b equal to when simplified?

a⁸ ÷ a⁴b Signup and view all the answers

What does ½a⁹ equal?

6a¹³ ÷ 12a⁴ Signup and view all the answers

What is 9a³ equal to?

90a⁹ ÷ 10a⁶ Signup and view all the answers

What is equivalent to 1?

x² ÷ x² Signup and view all the answers

What does a⁶ equal?

(a³)² Signup and view all the answers

How can 64a²¹ be expressed?

(4a⁷)³ Signup and view all the answers

What is a⁸b¹² equivalent to?

(a²b³)⁴ Signup and view all the answers

What does a⁵⁴ equal?

(a⁹)⁶ Signup and view all the answers

What is 6a²¹ equal to?

(2a⁷)³ Signup and view all the answers

What is 144a¹⁶ equivalent to?

(12a⁸)² Signup and view all the answers

How can a²¹ be expressed?

(a⁷)³ Signup and view all the answers

What does a⁶b¹⁴ equal?

(a³b⁷)² Signup and view all the answers

How can 16a⁸ be expressed?

(4a⁴)² Signup and view all the answers

What is a³⁵ equal to?

(a⁷)⁵ Signup and view all the answers

What is the value of 2?

x⁰ + x⁰ Signup and view all the answers

How can 8 be expressed?

8a⁰ Signup and view all the answers

What is the value of 0?

3⁰ - a⁰ Signup and view all the answers

How can 6 + a be expressed?

8e⁰ - 2a⁰ + a Signup and view all the answers

Study Notes

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.

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Description

This quiz focuses on the properties of exponents and the manipulation of algebraic indices. It includes various examples illustrating how to multiply and combine terms with different powers. Perfect for reinforcing your understanding of exponent rules and algebraic expressions.