How do you evaluate $48^{\frac{4}{3}} \cdot 8^{\frac{2}{3}} \cdot {(\frac{1}{6^{2}})}^{\frac{3}{2}}$ $48^(4/3)8^(2/3)(1/6^2)^(3/2)$ ?

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How do you evaluate $48^{\frac{4}{3}} \cdot 8^{\frac{2}{3}} \cdot {(\frac{1}{6^{2}})}^{\frac{3}{2}}$ $48^(4/3)8^(2/3)(1/6^2)^(3/2)$ ?

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Answer 1 · 2016-05-02T05:49:22

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

Explanation:

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

= ${(2 \times 2 \times 2 \times 2 \times 3)}^{\frac{4}{3}} \cdot {(2 \times 2 \times 2)}^{\frac{2}{3}} \cdot {({(2 \times 3)}^{- 2})}^{\frac{3}{2}}$ $(2xx2xx2xx2xx3)^(4/3)* (2xx2xx2)^(2/3)*((2xx3)^(-2))^(3/2)$

= ${(2^{4} \times 3)}^{\frac{4}{3}} \cdot {(2^{3})}^{\frac{2}{3}} \cdot {(2 \times 3)}^{- 2 \times \frac{3}{2}}$ $(2^4xx3)^(4/3)* (2^3)^(2/3)*(2xx3)^(-2xx3/2)$

= $2^{4 \times \frac{4}{3}} \cdot 3^{\frac{4}{3}} \cdot 2^{3 \cdot \frac{2}{3}} \cdot {(2 \times 3)}^{- 3}$ $2^(4xx4/3)*3^(4/3)*2^(3*2/3)*(2xx3)^(-3)$

= $2^{\frac{16}{3}} \cdot 3^{\frac{4}{3}} \cdot 2^{2} \cdot 2^{- 3} \cdot 3^{- 3}$ $2^(16/3)* 3^(4/3)* 2^2*2^(-3)*3^(-3)$

= $2^{\frac{16}{3} + 2 - 3} \times 3^{\frac{4}{3} - 3}$ $2^(16/3+2-3)xx3^(4/3-3)$

= $2^{\frac{13}{3}} \times 3^{- \frac{1}{3}}$ $2^(13/3)xx3^(-1/3)$

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

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How do you evaluate $48^{\frac{4}{3}} \cdot 8^{\frac{2}{3}} \cdot {(\frac{1}{6^{2}})}^{\frac{3}{2}}$ $48^(4/3)8^(2/3)(1/6^2)^(3/2)$ ?

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How do you evaluate $48^{\frac{4}{3}} \cdot 8^{\frac{2}{3}} \cdot {(\frac{1}{6^{2}})}^{\frac{3}{2}}$ $48^(4/3)8^(2/3)(1/6^2)^(3/2)$ ?