Simplifying Rational Expressions Answers

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Simplify each expression.

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Simplify each expression.

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The exponent on x is [___].

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4

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Describe how you would simplify the given expression.

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To simplify the expression, first simplify inside the parentheses by dividing the coefficients (20/5 = 4) and subtracting the exponents for each base (5 - (-3) = 8 for x, and 2 - 7 = -5 for y), which results in 4x^8y^-5. Next, raise the resulting expression to the -3 power by multiplying the exponents (8 * -3 = -24 and -5 * -3 = 15). Finally, rewrite the expression using positive exponents. Alternatively, you could first raise the numerator and denominator to the -3 power using the power of a power property, then divide coefficients and subtract exponents.

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Simplify. Express the answers using positive exponents.

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Answers:

Blank 1:4

Blank 2:14

Blank 3:4

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Type "numerator" or "denominator" to complete each statement.

Answers:

Blank 1:numerator

Blank 2:denominator

Blank 3:denominator

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Examine Tamika’s work below. What is Tamika’s error?

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She added the exponents.

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She simplified the coefficients incorrectly.

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She divided the exponents.

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She moved bases with positive exponents.

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Simplify. Express the answers using positive exponents.

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Simplify each expression.

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Simplify each expression.

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Simplify the given expression, using only positive exponents. Then complete the statements that follow. [ (x2y3)−1 (x−2y2z)2 ] 2 , x ≠ 0, y ≠ 0, z ≠ 0. The exponent on x is . The exponent on y is . The exponent on z is .

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Blank 1:4

Blank 2:14

Blank 3:4

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Simplify the given expression, using only positive exponents. Then complete the statements that follow. [ (x2y3)−1 (x−2y2z)2 ] 2 , x ≠ 0, y ≠ 0, z ≠ 0. The exponent on x is . The exponent on y is . The exponent on z is .

Answers:

Blank 1:numerator

Blank 2:denominator

Blank 3:denominator

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Examine Tamika’s work below. What is Tamika’s error?

A

She added the exponents.

B

She simplified the coefficients incorrectly.

C

She divided the exponents.

D

She moved bases with positive exponents.

1

Describe how you would simplify the given expression.

Answer:

To simplify the expression, first simplify inside the parentheses by dividing the coefficients (20/5 = 4) and subtracting the exponents for each base (5 - (-3) = 8 for x, and 2 - 7 = -5 for y), which results in 4x^8y^-5. Next, raise the resulting expression to the -3 power by multiplying the exponents (8 * -3 = -24 and -5 * -3 = 15). Finally, rewrite the expression using positive exponents. Alternatively, you could first raise the numerator and denominator to the -3 power using the power of a power property, then divide coefficients and subtract exponents.

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Which did you include in your response?

A

Simplify inside the parentheses by dividing coefficients, subtracting the exponents on like bases, and raising the resulting expression to the –3 power. Then, write bases with positive exponents.

B

Raise the numerator and denominator to the –3 power. Then, using the power of a power property, multiply the exponents. Divide the coefficients and subtract the exponents on like bases, then write with positive exponents.

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Which did you include in your response?Simplify inside the parentheses by dividing coefficients, subtracting the exponents on like bases, and raising the resulting expression to the –3 power. Then, write bases with positive exponents.Raise the numerator and denominator to the –3 power. Then, using the power of a power property, multiply the exponents. Divide the coefficients and subtract the exponents on like bases, then write with positive exponents.

A

Simplify inside the parentheses by dividing coefficients, subtracting the exponents on like bases, and raising the resulting expression to the –3 power. Then, write bases with positive exponents.

B

Raise the numerator and denominator to the –3 power. Then, using the power of a power property, multiply the exponents. Divide the coefficients and subtract the exponents on like bases, then write with positive exponents.

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The exponent on y is [___].

Answer:

14

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