Exam 9: Rational Exponents

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Combine the complex numbers. Combine the complex numbers.

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Find x and y so that the following equation is true. Find x and y so that the following equation is true.

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Find x and y so that the following equation is true. Find x and y so that the following equation is true.

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Solve the equation. (Hint: square both sides of the equation twice to eliminate the radicals.) Solve the equation. (Hint: square both sides of the equation twice to eliminate the radicals.)   x = __________ x = __________

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Simplify the expression. Do not assume that the variables represent positive numbers. Simplify the expression. Do not assume that the variables represent positive numbers.

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Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive. Use the properties of exponents to simplify the following as much as possible. Assume all bases are positive.

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Simplify the expression. Remember, negative exponents give reciprocals. Simplify the expression. Remember, negative exponents give reciprocals.

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Rationalize the denominator in the following: Rationalize the denominator in the following:

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Use Property 1 for Radicals to write the expression in simplified form. Use Property 1 for Radicals to write the expression in simplified form.

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Combine the expressions. (Assume the variables are nonnegative numbers.) Combine the expressions. (Assume the variables are nonnegative numbers.)

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Solve the equation. Solve the equation.

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Factor the expression as if it were a trinomial. Factor the expression as if it were a trinomial.

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Multiply. (Assume the variables represent nonnegative real numbers.) Multiply. (Assume the variables represent nonnegative real numbers.)

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Simplify the expression to a single fraction. Simplify the expression to a single fraction.

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Simplify the expression. Remember, negative exponents give reciprocals. Simplify the expression. Remember, negative exponents give reciprocals.

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Rationalize the denominator in the following expression. Rationalize the denominator in the following expression.

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Multiply. Multiply.

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Combine the expressions. (Assume the variables are nonnegative numbers.) Combine the expressions. (Assume the variables are nonnegative numbers.)

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Graph the equation. Graph the equation.

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Combine the expressions. Combine the expressions.

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