What is the reciprocal of $$\frac{3}{4}$$ ?

The reciprocal of $$\frac{3}{4}$$ is $$\frac{4}{3}$$ .

What does $$x^{\frac{5}{4}} = 243$$ imply?

It implies that you can rewrite it as $$x = 243^{\frac{4}{5}}$$ .

What is the first step in solving $$\text{If } (x-27)^{\frac{3}{2}} = 64$$ ?

Isolate the term with the exponent: $$(x-27)^{\frac{3}{2}} = 64$$ .

How do you rewrite $$(2x + 1)^{\frac{3}{4}}$$ for solving?

You can express it as $$\text{Let } y = (2x + 1)^{\frac{3}{4}}$$ .

What is the significance of the denominator in a rational exponent?

The denominator indicates the root to be taken. For example, in $$x^{\frac{1}{3}}$$ , you take the cube root of x.

What does $$\text{If } (2x - 5)^{\frac{1}{3}} = 3$$ imply about x?

It implies that you can find x by cubing both sides and solving for x.

What is the general form of a rational exponent equation?

The general form is $$a^{\frac{m}{n}} = b$$ , where a is the base, m is the numerator, and n is the denominator.

Solving Equations with Rational Exponents Including X Flashcards

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1.

FLASHCARD QUESTION

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What is a rational exponent?

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2.

FLASHCARD QUESTION

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How do you solve an equation with a rational exponent?

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To solve an equation with a rational exponent, isolate the variable term and then raise both sides of the equation to the reciprocal of the rational exponent.

3.

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4.

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5.

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6.

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7.

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