Solving Equations with Rational Exponents

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
+1
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What is a rational exponent?
Back
A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root. For example, x^(1/2) is the square root of x.
Tags
CCSS.HSN.RN.A.2
2.
FLASHCARD QUESTION
Front
How do you solve an equation with a negative rational exponent?
Back
To solve an equation with a negative rational exponent, first rewrite the expression using a positive exponent. For example, x^(-3/4) = 1/(x^(3/4)). Then solve for x.
3.
FLASHCARD QUESTION
Front
What is the first step in solving x^(-3/4) = 8?
Back
Rewrite the equation as 1/(x^(3/4)) = 8, then multiply both sides by x^(3/4) to isolate x.
4.
FLASHCARD QUESTION
Front
If (x-2)^(1/3) = 5, what is the next step to solve for x?
Back
Cube both sides of the equation to eliminate the exponent: x - 2 = 5^3.
5.
FLASHCARD QUESTION
Front
What does it mean to cube a number?
Back
Cubing a number means raising it to the power of three, which is multiplying the number by itself three times.
Tags
CCSS.8.EE.A.2
6.
FLASHCARD QUESTION
Front
How do you isolate x in the equation 2x^(3/4) = 54?
Back
Divide both sides by 2 to get x^(3/4) = 27, then raise both sides to the power of 4/3 to solve for x.
7.
FLASHCARD QUESTION
Front
What is the solution to the equation x^(1/3) - 7 = 0?
Back
Add 7 to both sides to get x^(1/3) = 7, then cube both sides to find x = 343.
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