How do you simplify ${(8^{\frac{5}{3}})}^{\frac{2}{5}}$ $(8 ^(5/3)) ^(2/5)$ ?

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Answer 1 · 2016-03-25T05:03:31

$4$ $4$

${(8^{\frac{5}{3}})}^{\frac{2}{5}}$ $color(blue)((8^(5/3))^(2/5)$

Use law of exponents

${(x^{y})}^{z} = x^{x y}$ $color(brown)((x^y)^z=x^(xy)$

$:.(8^(5/3))^(2/5)=8^(5/3*2/5)$

$rarr=8^(10/15)$

$color(purple)(rArr8^(2/3)$

But we are not finished yet,

Solve for $8^(2/3)$

Use law of exponents

$color(brown)(x^(y/z)=root(z)(x^y$

$:.color(green)(8^(2/3)=root(3)(8^2)=root(3)(64)=4$

How do you simplify (8 ^(5/3)) ^(2/5)(853)25(8 ^(5/3)) ^(2/5)?