# How do you evaluate and simplify (12^(3/5)*8^(3/5))^5?

Aug 31, 2016

$884736$.

#### Explanation:

The Expression$= {\left({12}^{\frac{3}{5}} \cdot {8}^{\frac{3}{5}}\right)}^{5}$

$= {\left({12}^{\frac{3}{5}}\right)}^{5} \cdot {\left({8}^{\frac{3}{5}}\right)}^{5.} \ldots \ldots \ldots \ldots . . \left[\text{Rule} : {\left(a b\right)}^{m} = {a}^{m} . {b}^{m}\right]$

$= {12}^{\left(\frac{3}{5} \cdot 5\right)} \cdot {8}^{\left(\frac{3}{5} \cdot 5\right)} \ldots \ldots \ldots \ldots \left[\text{Rule} : {\left({a}^{m}\right)}^{n} = {a}^{\left(m \cdot n\right)}\right]$

$= {12}^{3} \cdot {8}^{3}$

$= 1728 \cdot 512 = 884736$.

Alternatively,

The Expression$= {\left({12}^{\frac{3}{5}} \cdot {8}^{\frac{3}{5}}\right)}^{5}$

$= {\left\{{\left(12 \cdot 8\right)}^{\frac{3}{5}}\right\}}^{5.} \ldots \ldots \ldots \ldots \ldots . . \left[\text{Rule} : {a}^{m} \cdot {b}^{m} = {\left(a b\right)}^{m}\right]$

$= {\left(96\right)}^{\frac{3}{5} \cdot 5} \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . \left[\text{Rule} : {\left({a}^{m}\right)}^{n} = {a}^{\left(m \cdot n\right)}\right]$

$= {96}^{3}$

$= {\left(100 - 4\right)}^{3}$.

Here, we use, ${\left(x - y\right)}^{3} = {x}^{3} - {y}^{3} - 3 x y \left(x - y\right)$, and get,

${96}^{3} = {100}^{3} - {4}^{3} - 3 \left(100\right) \left(4\right) \left(100 - 4\right)$

$= 1000000 - 64 - 1200 \left(100 - 4\right)$

$= 1000000 - 64 - 120000 + 4800$

$= 1004800 - 120064$

$= 884736$, as before!

Enjoy Maths.!