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?
- -4
- -2
- -2
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?
- Rationalizing the denominator (correct)
- Factoring
- Radical decomposition
- Rearranging
Which of the following is irrational?
Which of the following is irrational?
- ³√16 (correct)
- ³√343
- ³√8
- 3√1000 (correct)
Which statement is equivalent except for one?
Which statement is equivalent except for one?
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?
What is the difference when 8√12a is subtracted by 5√12a?
What is the difference when 8√12a is subtracted by 5√12a?
Which is equal to (a³b³)⁴?
Which is equal to (a³b³)⁴?
What is the value of k if a²–¹ =a?
What is the value of k if a²–¹ =a?
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?
Flashcards
Sum of exponents
Sum of exponents
When multiplying terms with the same base, add their exponents.
Rationalizing the denominator
Rationalizing the denominator
A process of eliminating radicals (square roots) from the denominator of a fraction.
Like radicals
Like radicals
Radicals with the same radicand (number under the square root symbol).
Inverse variation
Inverse variation
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Direct variation
Direct variation
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Irrational number
Irrational number
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Power of a product
Power of a product
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Joint variation
Joint variation
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Constant of variation
Constant of variation
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Radical expression
Radical expression
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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
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