Algebraic Fractions Unit 5 Flashcards

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

State the value of the expression (In Fraction Form): (55x^2)^0

State the value of the expression (In Fraction Form): (2^-3) + (4^-3)

9/64

State the value of the expression (In Fraction Form): (4^0) + (6^-3)

1 1/216

State the value of the expression (In Fraction Form): (1)/[(2^0)-(2^1)]

-1 Signup and view all the answers

Express with positive exponents (In Fraction Form and in Simplified Form): 4(x+y)^-1

4/(x+y) Signup and view all the answers

Express with positive exponents (In Fraction Form and in Simplified Form): (x^6n)/(x^3n)

x^3 Signup and view all the answers

Express with positive exponents (In Fraction Form and in Simplified Form): [(5x^3)^-2]/(2)

1/(25x^6) Signup and view all the answers

Express with positive exponents (In Fraction Form and in Simplified Form): (8x^3)^-3

1/(512x^9) Signup and view all the answers

Reduce the Algebraic Fraction and state the exclusion for: (60x^3)/(12x)

5x^2; x≠0 Signup and view all the answers

Reduce the Algebraic Fraction and state the exclusion for: (24x^2 yz^4)/(8x^3 y^8 z)

-3z^3/xy^7; x≠0, y≠0, z≠0 Signup and view all the answers

Reduce the Algebraic Fraction and state the exclusion for: (70x^2)/(100x)

7x/10; x≠0 Signup and view all the answers

Reduce the Algebraic Fraction and state the exclusion for: (26x^2 y^6 z^8)/(4x^6 z^10)

(13y^6)/(2x^4 z^2); x≠0, z≠0 Signup and view all the answers

Reduce the Algebraic Fraction and state the exclusion for: (x+7)/(x^2 +4m-21)

1/(x-3); x≠-7, x≠3 Signup and view all the answers

Reduce the Algebraic Fraction and state the exclusion for: (-x^2 +16x-63)/(x^2 -2x-35)

(-x+9)/(x+5); x≠7, x≠-5 Signup and view all the answers

Reduce the Algebraic Fraction and state the exclusion for: (5x-2)/(5x-2)

1; x≠(2/5) Signup and view all the answers

Reduce the Algebraic Fraction and state the exclusion for: (x-x^4)/(x^2 +x+1)

x-x^2; none Signup and view all the answers

Reduce the Algebraic Fraction and state the exclusion for: [(x+y)^-6]/[(x+y)^-10]

(x+y)^4; x≠-y, y≠-x Signup and view all the answers

Multiply or divide the algebraic expression: [(4x)/(5y)]*[(3a)/(4b)]

3ax/5by Signup and view all the answers

Multiply or divide the algebraic expression: [(15x^2 y^3)/(8z^3)]*[(16z^5)/(35xy^4)]

(6xz^2)/(7y) Signup and view all the answers

Multiply or divide the algebraic expression: [(x^2 -4x+4)/(x-6)]*[(x^2 -36)/(x^2 -8x+12)]

(x-2)(x-6)/(x-6) Signup and view all the answers

Multiply or divide the algebraic expression: [(x+4)/(x^2 -1)]*[(x^2 +3x-28)/(x^2 -16)]

(x+7)/(x+1)(x-1) Signup and view all the answers

Multiply or divide the algebraic expression: [(x^2 y)/(xy^2)]/[(x^2)/(y)]

1/x Signup and view all the answers

Multiply or divide the algebraic expression: [(40x^2 y^2)/(8z)]/(8xy)

5xy/8z Signup and view all the answers

Multiply or divide the algebraic expression: {[y^2 -16]/[(y+4)(y+4)]}/{[7y-28]/[3y+12]}

3/7 Signup and view all the answers

Multiply or divide the algebraic expression: [(2x^2 -18)/(x^2 -8x+15)]/[(10x+30)/(5x-15)]

(x-3)/(x-5) Signup and view all the answers

Study Notes

Algebraic Fractions Review

Expressions raised to the power of zero, like (55x^2)^0, equal 1, regardless of the base.
For the expression (2^-3)+(4^-3), the value simplifies to 9/64.
The expression (4^0)+(6^-3) simplifies to 1 1/216, combining a constant and a power of a fraction.
The expression (1)/[(2^0)-(2^1)] simplifies to -1, as 2^0 equals 1 and 2^1 equals 2.

Positive Exponents

To express 4(x+y)^-1 with positive exponents, the formulation becomes 4/(x+y).
Simplifying (x^6n)/(x^3n) yields x^3 since the exponents subtract (6-3).
For [(5x^3)^-2]/(2), the result is 1/25x^6 after applying negative exponents.
(8x^3)^-3 also simplifies to 1/512x^9 using negative exponent rules.

Reducing Algebraic Fractions

The fraction (60x^3)/(12x) simplifies to 5x^2 with the exclusion x≠0.
From (24x^2 yz^4)/(8x^3 y^8 z), the reduction yields -3z^3/xy^7 with exclusions x≠0, y≠0, z≠0.
The expression (70x^2)/(100x) simplifies to 7x/10 with exclusion x≠0.
(26x^2 y^6 z^8)/(4x^6 z^10) reduces to (13y^6)/(2x^4 z^2) with exclusions x≠0, z≠0.

Exclusion and Restrictions

The fraction (x+7)/(x^2 +4m-21) simplifies to 1/(x-3), with restrictions x≠-7, x≠3.
From (-x^2 +16x-63)/(x^2 -2x-35), the reduction results in (-x+9)/(x+5), with x≠7, x≠-5.
(5x-2)/(5x-2) simplifies to 1 with exclusion x≠(2/5).
The expression (x-x^4)/(x^2 +x+1) simplifies to x-x^2, with no exclusions.

Further Reductions

The fraction [(x+y)^-6]/[(x+y)^-10] simplifies to (x+y)^4, with exclusions x≠-y, y≠-x.
[(4x)/(5y)]*[(3a)/(4b)] results in 3ax/5by by multiplying numerators and denominators.
For the product of two fractions, [(15x^2 y^3)/(8z)]*[(16z^5)/(35xy^4)], the result is (6xz^2)/(7y).

Factored Forms

The expression [(x^2 -4x+4)/(x-6)]*[(x^2 -36)/(x^2 -8x+12)] simplifies to (x-2)(x-6)/(x-6).
The product of fractions [(x+4)/(x^2 -1)]*[(x^2 +3x-28)/(x^2 -16)] results in (x+7)/(x+1)(x-1).
Dividing [(x^2 y)/(xy^2)] by [(x^2)/(y)] yields 1/x.
Multiplying and dividing {(y^2 -16)/[(y+4)(y+4)]}/{[7y-28]/[3y+12]} results in 3/7.
For {(2x^2 -18)/(x^2 -8x+15)} / {(10x+30)/(5x-15)}, the resulting simplification is (x-3)/(x-5).

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Review essential concepts in algebraic fractions with these flashcards. Each card presents an algebraic expression that you need to evaluate in fraction form. Perfect for quick revision and reinforcing understanding of algebraic principles.