Worksheet (with Solutions): Rational Exponents And Radicals

Section A: Multiple Choice Questions

Q1: Simplify the expression \(x^{\frac{2}{3}} \cdot x^{\frac{1}{3}}\)
(a) \(x^{\frac{2}{9}}\)
(b) \(x\)
(c) \(x^{\frac{1}{3}}\)
(d) \(x^2\)

Q2: Which of the following is equivalent to \(\sqrt[4]{16x^8}\)?
(a) \(4x^2\)
(b) \(2x^2\)
(c) \(2x^4\)
(d) \(4x^4\)

Q3: Evaluate \(27^{\frac{2}{3}}\)
(a) 6
(b) 9
(c) 18
(d) 3

Q4: Simplify \(\frac{x^{\frac{5}{6}}}{x^{\frac{1}{6}}}\)
(a) \(x^{\frac{5}{36}}\)
(b) \(x^{\frac{2}{3}}\)
(c) \(x^{\frac{4}{6}}\)
(d) \(x\)

Q5: Which expression is equivalent to \(\sqrt[3]{x^6y^9}\)?
(a) \(x^3y^6\)
(b) \(x^2y^3\)
(c) \(x^2y^6\)
(d) \(x^3y^3\)

Q6: Simplify \((8x^6)^{\frac{1}{3}}\)
(a) \(2x^3\)
(b) \(2x^2\)
(c) \(8x^2\)
(d) \(4x^3\)

Q7: What is the value of \(16^{-\frac{3}{4}}\)?
(a) \(\frac{1}{8}\)
(b) \(-12\)
(c) \(\frac{1}{12}\)
(d) \(8\)

Q8: Simplify \(\sqrt{x} \cdot \sqrt[4]{x}\)
(a) \(x^{\frac{3}{4}}\)
(b) \(x^{\frac{1}{4}}\)
(c) \(x^2\)
(d) \(x^{\frac{5}{4}}\)

Section B: Fill in the Blanks

Section C: Word Problems