How do you simplify ${[{(2 x y^{3})}^{2}]}^{3}$ $[(2xy^3)^2]^3$ ?

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How do you simplify ${[{(2 x y^{3})}^{2}]}^{3}$ $[(2xy^3)^2]^3$ ?

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Answer 1 · 2017-01-19T01:24:35

${[{(2 x y^{3})}^{2}]}^{3} = 64 x^{6} y^{18}$ $[(2xy^3)^2]^3=64x^6y^18$

Explanation:

We will use the following properties of exponents:

${(x^{a})}^{b} = x^{a b}$ $(x^a)^b = x^(ab)$
${(x y)}^{a} = x^{a} y^{a}$ $(xy)^a = x^ay^a$

With those,

${[{(2 x y^{3})}^{2}]}^{3} = {(2 x y^{3})}^{2 \cdot 3}$ $[(2xy^3)^2]^3 = (2xy^3)^(2*3)$

$= {(2 x y^{3})}^{6}$ $=(2xy^3)^6$

$= 2^{6} x^{6} {(y^{3})}^{6}$ $=2^6x^6(y^3)^6$

$= 2^{6} x^{6} y^{3 \cdot 6}$ $=2^6x^6y^(3*6)$

$= 2^{6} x^{6} y^{18}$ $=2^6x^6y^18$

$= 64 x^{6} y^{18}$ $=64x^6y^18$

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How do you simplify ${[{(2 x y^{3})}^{2}]}^{3}$ $[(2xy^3)^2]^3$ ?

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