Exam 9: Rational Exponents

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

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Find the product. Find the product.

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Solve the equation. Solve the equation.   y = __________ y = __________

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

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

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

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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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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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Find the following root, if possible. Find the following root, if possible.

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Use Property 1 for Radicals to write the expression in simplified form. (Assume the variables are nonnegative numbers.) Use Property 1 for Radicals to write the expression in simplified form. (Assume the variables are nonnegative numbers.)

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

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The length of the diagonal of a rectangular box with length l , width w , and height h , is given by The length of the diagonal of a rectangular box with length l , width w , and height h , is given by   . Find the length of the diagonal of a rectangular box that is 5 feet wide, 8 feet long, and 12 feet high. Round your answer to the nearest tenth of a foot.  . Find the length of the diagonal of a rectangular box that is 5 feet wide, 8 feet long, and 12 feet high. Round your answer to the nearest tenth of a foot. The length of the diagonal of a rectangular box with length l , width w , and height h , is given by   . Find the length of the diagonal of a rectangular box that is 5 feet wide, 8 feet long, and 12 feet high. Round your answer to the nearest tenth of a foot.

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Use Property 1 for Radicals to write the expression in simplified form. (Assume the variables are nonnegative numbers.) Use Property 1 for Radicals to write the expression in simplified form. (Assume the variables are nonnegative numbers.)

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Combine the complex numbers. Combine the complex numbers.

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Multiply. Multiply.

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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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A long straight river, 36 meters wide, is flowing at 1 meter per second. A pollutant is entering the river at a constant rate from one of its banks. As the pollutant disperses in the water, it forms a plume that is modeled by the equation A long straight river, 36 meters wide, is flowing at 1 meter per second. A pollutant is entering the river at a constant rate from one of its banks. As the pollutant disperses in the water, it forms a plume that is modeled by the equation   . How wide is the plume 36 meters down river from the source of the pollution? . How wide is the plume 36 meters down river from the source of the pollution?

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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 Property 1 for Radicals to write the expression in simplified form. (Assume the variables are nonnegative numbers.) Use Property 1 for Radicals to write the expression in simplified form. (Assume the variables are nonnegative numbers.)

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