Podcast
Questions and Answers
What is the sum of the expression [-(2)⁰]+(-2)⁰?
What is the sum of the expression [-(2)⁰]+(-2)⁰?
What process is used to eliminate radicals from the denominator or fractions from a radicand?
What process is used to eliminate radicals from the denominator or fractions from a radicand?
Which of the following is irrational?
Which of the following is irrational?
Which statement is equivalent except for one?
Which statement is equivalent except for one?
Signup and view all the answers
If a varies jointly as b and c, and a = 24, b = 2, and c = 3, what equation represents this variation?
If a varies jointly as b and c, and a = 24, b = 2, and c = 3, what equation represents this variation?
Signup and view all the answers
What is the difference when 8√12a is subtracted by 5√12a?
What is the difference when 8√12a is subtracted by 5√12a?
Signup and view all the answers
Which is equal to (a³b³)⁴?
Which is equal to (a³b³)⁴?
Signup and view all the answers
What is the value of k if a²–¹ =a?
What is the value of k if a²–¹ =a?
Signup and view all the answers
Which law of exponents makes the statement $(3y)^{3/2} = 27^{1/3}y^{3/2}$ TRUE?
Which law of exponents makes the statement $(3y)^{3/2} = 27^{1/3}y^{3/2}$ TRUE?
Signup and view all the answers
Study Notes
Fractional Exponents and Radicals
- To convert expressions with fractional exponents to radicals, the numerator becomes the power and the denominator the root.
- (2x)3/5 is equivalent to ⁵√(2x)3.
Simplifying Radical Expressions
- Rationalizing the denominator involves eliminating radicals from the denominator of a fraction.
- Factoring and simplifying the radicand are often used.
Difference of Radicals
- Subtracting radicals involves finding like radicals.
- If radicals have the same index and radicand, subtract their coefficients
- example: 8√12a - 5√12a = 3√12a
Joint Variation
- Joint variation means a variable is proportional to the product of two other variables.
- For instance, a = kbc; thus 'a' varies directly as 'b' and 'c'
Inverse Variation
- In inverse variation, one variable changes inversely with another.
- If b varies inversely as a, then the product of a and b remains constant.
Laws of Exponents
- Rules relate to multiplying, dividing, or raising numbers with exponents.
- (xm)(xn) = xm+n
Simplifying Expressions
- Find the sum and difference of the expression by combining like radicals.
- 44/55 * 6100/73 is simplified by combining common elements.
Proportional Relationships
- Direct variation means two variables change in the same direction.
- (y = kx) is the equation demonstrating direct proportionality.
Determining the Constant of Variation
- Determine the constant of variation within a given equation or scenario.
- Ex. If y = 40 and x = 8, then the constant k is 5
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers the concepts of fractional exponents, simplifying radical expressions, and both joint and inverse variation. Test your understanding of how to manipulate and simplify expressions in algebraic contexts, and apply the laws of exponents effectively.
