Exam 9: Rational Exponents

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Combine the expressions. Combine the expressions.

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Find the product. Find the product.

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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.

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Multiply. (Assume all expressions appearing under a square root symbol represent nonnegative numbers.) Multiply. (Assume all expressions appearing under a square root symbol represent nonnegative numbers.)

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

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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.)

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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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Combine the expressions. Combine the expressions.

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

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Write the expression in simplified form. Write the expression in simplified form.

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Simplify the expression. Simplify the expression.

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Multiply. Multiply.

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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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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.

(Multiple Choice)
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Combine the expressions. Combine the expressions.

(Short Answer)
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Multiply. (Assume the variable represents a nonnegative real number.) Multiply. (Assume the variable represents a nonnegative real number.)

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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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Find the product. Find the product.

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Combine the expressions. Combine the expressions.

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Divide. Divide.

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