Name:			Date:
Simplifying the Rational Exponents.

1) ${\left(x^{11}\right)}^{\frac{3}{11}}$	2) ${\left(b^5\right)}^{\frac{2}{5}}$
3) ${\left(729x^3\right)}^{\frac{4}{3}}$	4) ${\left(625b^{12}\right)}^{0.25}$
5) ${\left(256a^{12}\right)}^{1.5}$	6) ${\left(64m^{12}\right)}^{0.17}$
7) $2y^6.8y^{\frac{5}{7}}.8y^{-6}$	8) $9n^{\frac{1}{8}}.n^{\frac{11}{3}}$
9) ${\left(b^{\frac{5}{2}}\right)}^{-2}$	10) $\frac{125m^7}{5m^{\frac{1}{7}}}$
11) ${(c^{-3}{d}^{\frac{1}{3}}.c^{\frac{-5}{3}}{d}^4)}^4$	12) $\frac{{\left(m^{\frac{-1}{3}}{n}^5\right)}^{\frac{1}{5}}}{m^{\frac{2}{5}}{n}^{\frac{8}{3}}.m^{\frac{-5}{2}}{n}^{\frac{1}{3}}}$
13) ${(u^{-6}{v}^{\frac{1}{9}}.u^{\frac{-5}{7}}{v}^2)}^6$	14) ${(r.r^{-4}{s}^{\frac{5}{3}})}^4$
15) ${(x.x^{-5}{y}^{\frac{2}{3}})}^5$	16) $\frac{{\left(r^5{s}^3\right)}^{\frac{5}{3}}}{{\left(r^{-1}{s}^{\frac{-3}{5}}\right)}^{\frac{1}{4}}}$

 

Answers:

1) $x^3$	2) $b^2$
3) $6561x^4$	4) $5b^3$
5) $4096a^{18}$	6) $2m^2$
7) $128y^{\frac{5}{7}}$	8) $9n^{\frac{91}{24}}$
9) $\frac{1}{b^5}$	10) $25m^{\frac{48}{7}}$
11) $\frac{c^{\frac{1}{3}}{d}^{\frac{52}{3}}}{c^{19}}$	12) $\frac{m^{\frac{61}{30}}}{n}$
13) $\frac{u^{\frac{5}{7}}{v}^{\frac{38}{3}}}{u^{41}}$	14) $\frac{s^{\frac{20}{3}}}{r^{12}}$
15) $\frac{y^{\frac{10}{3}}}{x^{20}}$	16) $s^{\frac{103}{20}}{r}^{\frac{103}{12}}$