Exam 9: Rational Exponents

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

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Write the number in terms of i , and simplify as much as possible. Write the number in terms of i , and simplify as much as possible.

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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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Divide. Divide.

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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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If an object is dropped from the top of a 121-foot building, the amount of time t (in seconds) that it takes for the object to be h feet from the ground is given by the formula If an object is dropped from the top of a 121-foot building, the amount of time t (in seconds) that it takes for the object to be h feet from the ground is given by the formula   How long does it take before the object is 71 feet from the ground? How long does it take to reach the ground? (When it is on the ground, h is 0.) How long does it take before the object is 71 feet from the ground? How long does it take to reach the ground? (When it is on the ground, h is 0.)

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Solve the equation. Solve the equation.

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Find the product. Find the product.

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

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Substitute the given numbers a = 4, b = 5, c = - 6 into the expression Substitute the given numbers a = 4, b = 5, c = - 6 into the expression   and simplify. and simplify.

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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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Combine the complex numbers. Combine the complex numbers.

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Combine the expressions. Combine the expressions.

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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 product. Find the product.

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Solve the equation. Solve the equation.

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

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