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

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Answer 1 · 2016-03-25T05:03:31

#4#

#color(blue)((8^(5/3))^(2/5)#

Use law of exponents

#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#