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Lesson 2: Properties of Rational Exponents and Radicals — Practice Questions

  1. 1. Find the product: $(2x^{1/4} + 1)(x^{1/4} - 1)$.

    • A. $2x^{1/2} - x^{1/4} - 1$
    • B. $2x^{1/2} - 1$
    • C. $2x^{1/16} - x^{1/4} - 1$
    • D. $2x^{1/4} - 1$
  2. 2. Factor out the smallest power from the expression $x^{3/2} + x$. The result is $x(\_\_\_)$.

  3. 3. Use the distributive law to find the product: $3y^{-3/8}\left(\frac{1}{4}y^{-1/4} + y^{3/4}\right)$.

    • A. $\frac{3}{4}y^{-5/8} + 3y^{3/8}$
    • B. $\frac{3}{4}y^{3/32} + 3y^{-9/32}$
    • C. $\frac{3}{4}y^{-4/12} + 3y^{0}$
    • D. $\frac{3}{4}y^{-1/2} + 3y^{3/8}$
  4. 4. Simplify the expression by applying the laws of exponents. Write your answer with positive exponents only. $e^{-2/3}\left(\frac{2}{3}e^2\right) = \_\_\_$

  5. 5. Use the distributive law to find the product: $x^{1/3}(2x^{2/3} + x^{1/3})$.

    • A. $2x + x^{2/3}$
    • B. $2x^{2/9} + x^{1/9}$
    • C. $3x$
    • D. $2x + x^{1/3}$
  6. 6. Simplify the expression by applying the laws of exponents. Write your answer with positive exponents only. $(-3u^{5/3})(5u^{-2/3}) = \_\_\_$

  7. 7. Simplify the expression $\frac{n^{3/4}}{4n^{3/4}}$ by applying the laws of exponents. The simplified expression is ___.

  8. 8. Factor out the smallest power from the expression $a^{1/3} + 3 - a^{-1/3}$. The result is $a^{-1/3}(\_\_\_)$.

  9. 9. Factor out the smallest power from the expression $y^{3/4} - y^{-1/4}$. The result is $y^{-1/4}(\_\_\_)$.

  10. 10. An egg's water loss rate is $W(m) = 0.015m^{0.742}$ and incubation time is $I(m) = 12.0m^{0.217}$. The fraction of mass lost is $\frac{W(m)I(m)}{m} = km^p$. What is the value of $p$?

    • A. -0.041
    • B. 0.959
    • C. -0.959
    • D. 0.525