# How do you evaluate  48^(4/3)*8^(2/3)*(1/6^2)^(3/2) ?

May 2, 2016

${48}^{\frac{4}{3}} \cdot {8}^{\frac{2}{3}} \cdot {\left(\frac{1}{6} ^ 2\right)}^{\frac{3}{2}} = {2}^{\frac{13}{3}} / {3}^{\frac{1}{3}}$

#### Explanation:

${48}^{\frac{4}{3}} \cdot {8}^{\frac{2}{3}} \cdot {\left(\frac{1}{6} ^ 2\right)}^{\frac{3}{2}}$

= ${\left(2 \times 2 \times 2 \times 2 \times 3\right)}^{\frac{4}{3}} \cdot {\left(2 \times 2 \times 2\right)}^{\frac{2}{3}} \cdot {\left({\left(2 \times 3\right)}^{- 2}\right)}^{\frac{3}{2}}$

=${\left({2}^{4} \times 3\right)}^{\frac{4}{3}} \cdot {\left({2}^{3}\right)}^{\frac{2}{3}} \cdot {\left(2 \times 3\right)}^{- 2 \times \frac{3}{2}}$

= ${2}^{4 \times \frac{4}{3}} \cdot {3}^{\frac{4}{3}} \cdot {2}^{3 \cdot \frac{2}{3}} \cdot {\left(2 \times 3\right)}^{- 3}$

= ${2}^{\frac{16}{3}} \cdot {3}^{\frac{4}{3}} \cdot {2}^{2} \cdot {2}^{- 3} \cdot {3}^{- 3}$

= ${2}^{\frac{16}{3} + 2 - 3} \times {3}^{\frac{4}{3} - 3}$

= ${2}^{\frac{13}{3}} \times {3}^{- \frac{1}{3}}$

= ${2}^{\frac{13}{3}} / {3}^{\frac{1}{3}}$