Exercises for Question Type 2: Simplifying algebraic expressions involving rational exponents - IB | RevisionDojo

Question Type 2: Simplifying algebraic expressions involving rational exponents Exercises

Question 1

Simplify the expression $\sqrt{x}\cdot\sqrt[3]{x^2}$ and express your answer as a single power of $x$ .

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Question 2

Simplify the expression $(x^3 y^{-2})^{\frac{2}{3}}$ .

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Question 3

Algebraic expressions and index laws.

Simplify the expression $\dfrac{(2x^{1/4}y^{1/2})^4}{8xy^2}$ .

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Question 4

Simplify the expression $\dfrac{8x^{3/2}y^{-1/2}}{2x^{1/2}y^{1/2}}$ .

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Question 5

Standard algebraic simplification involving laws of exponents.

Simplify the expression $(64a^{-2}b^3)^{\frac{2}{3}}$ .

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Question 6

Simplify the expression $(x^{-1/2}y^{1/3})^{-3}$ .

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Question 7

Simplify the expression $x^{1/2}\cdot x^{1/3}$ and express your answer as a single power of $x$ .

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Question 8

Simplify the expression: $\left(\frac{x^{4/5}y^{2/5}}{x^{1/5}y^{3/5}}\right)^{5/2}$ giving your answer with positive exponents.

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Question 9

Simplify the expression $\left(\dfrac{x^{2/3}}{x^{1/6}}\right)^3$ .

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Question 10

Simplify the expression $(\sqrt[3]{x^2})^{-3}$ and express your answer using positive rational exponents.

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Question 11

Simplify the expression $\dfrac{16^{3/4}}{8^{1/3}}$ .

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Question 12

Simplify the expression $27^{2/3}\cdot9^{1/2}$ .

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