Exercises - Exponents

$\newcommand{\ds}[1]{\displaystyle{#1}}$

1. Simplify:

1. $\displaystyle{(-4a^{-2}b^4)^2(-a^2b^{-4}c)^3(ab^{-3}c^4)^2}$   $\ans{\displaystyle{\frac{-16a^4c^{11}}{b^{10}}}}$

2. $\displaystyle{\frac{18xy^3z^{-5}}{27x^{-2}y^2z^2}}$   $\ans{\displaystyle{\frac{2x^3y}{3z^7}}}$

3. $\displaystyle{\left[ \frac{-5x^{-3}}{(16y^2)^{-1/2}} \right]^{-1}}$   $\ans{\displaystyle{\frac{-x^3}{20y}}}$

4. $\displaystyle{(3x^2y^3)(-2x^{-3}y^2)(xy^2z^{1/3})^0}$   $\ans{\displaystyle{\frac{-6y^5}{x}}}$

5. $\displaystyle{(a+b)^{2/3}(a+b)}$   $\ans{\displaystyle{(a+b)^{5/3}}}$

6. $\displaystyle{\frac{(3x^{-1/2}y^{2/3})^{-2}}{(xy^{-1})^{-3}}}$   $\ans{\displaystyle{\frac{x^4}{9y^{13/3}}}}$

7. $\displaystyle{(7a^2 b^4)(-2a^{-4} b^3)}$   $\ans{\displaystyle{\frac{-14b^7}{a^2}}}$

8. $\displaystyle{(4x^4 y^{-2})(-3x^5 y^{-4})}$   $\ans{\displaystyle{-\frac{12x^9}{y^6}}}$

9. $\displaystyle{\frac{24pq^8 r^{-4}}{36 p^{-3} q^{-6} r^5}}$   $\ans{\displaystyle{\frac{2p^4q^{14}}{3r^9}}}$

10. $\displaystyle{\frac{54 x^6 y^{-4} z^2}{9x^{-3} y^2 z^{-4}}}$   $\ans{\displaystyle{\frac{6x^9z^6}{y^6}}}$

11. $\displaystyle{\left( \frac{25a^6 b^{-2}}{16x^4 a^4} \right)^{-\frac{1}{2}}}$   $\ans{\displaystyle{\frac{4bx^2}{5a}}}$

12. $\displaystyle{\left( \frac{25xy^{-2}}{16a^4b^6} \right)^{-\frac{1}{2}}}$   $\ans{\displaystyle{\frac{4a^2 b^3 y \sqrt{x}}{5x}}}$

13. $\displaystyle{\frac{(2k^2 rt)^{-2}}{(3k^{-1} r^{-2} t^3 )^{-1}}}$   $\ans{\displaystyle{\frac{3t}{4k^5r^4}}}$

14. $\displaystyle{\left( \frac{27x^2}{w^6} \right)^{-\frac{1}{3}}}$   $\ans{\displaystyle{\frac{w^2\sqrt[3]{x}}{3x}}}$

15. $\displaystyle{y^3 \cdot \left( \frac{45x^{-2} y^3 (zw^{-1})^0}{(-3)^3 x^{-4} y^{-2} w z^3} \right)^{-2}}$   $\ans{\displaystyle{\frac{9 w^2 z^6}{25 x^4 y^7}}}$

16. $\displaystyle{\left( \frac{16^{-1/4} + (-4)^{-2} - 2^{-3}}{8^{1/3}} \right)^{-1}}$   $\ans{\displaystyle{\frac{32}{7}}}$