Exam 9: Rational Exponents

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Combine the expressions. Combine the expressions.

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Simplify the expression. Assume all variables represent nonnegative numbers. Simplify the expression. Assume all variables represent nonnegative numbers.

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Combine the expressions. Combine the expressions.

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Combine the expressions. Combine the expressions.

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Factor Factor   from  from Factor   from

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Solve the equation. Solve the equation.   x = __________ x = __________

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Simplify the expression. Assume all variables represent nonnegative numbers. Simplify the expression. Assume all variables represent nonnegative numbers.

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Graph the equation. Graph the equation.

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Factor Factor   from  from Factor   from

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Use the definition of rational exponents to write the following with the appropriate root. Then simplify. Use the definition of rational exponents to write the following with the appropriate root. Then simplify.

(Multiple Choice)
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Rationalize the denominator in the following expression . (Assume all expressions appearing under a square root symbol represent nonnegative numbers.) Rationalize the denominator in the following expression . (Assume all expressions appearing under a square root symbol represent nonnegative numbers.)

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Use a calculator to find decimal approximations for Use a calculator to find decimal approximations for   and   . Give answers to three decimal places. and Use a calculator to find decimal approximations for   and   . Give answers to three decimal places. . Give answers to three decimal places.

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Find the quotient. Write the answer in standard form for complex numbers. Find the quotient. Write the answer in standard form for complex numbers.

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Find the following root, if possible. If impossible, write not a real number. Find the following root, if possible. If impossible, write not a real number.

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Combine the expressions. Combine the expressions.

(Multiple Choice)
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Rationalize the denominator in the following expression. (Assume all expressions appearing under a square root symbol represent nonnegative numbers.) Rationalize the denominator in the following expression. (Assume all expressions appearing under a square root symbol represent nonnegative numbers.)

(Short Answer)
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Find the following root, if possible. Find the following root, if possible.

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

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Substitute the given numbers a = 9, b = 7, c = - 2 into the expression Substitute the given numbers a = 9, b = 7, c = - 2 into the expression   and simplify. and simplify.

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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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