How do you simplify ${(3 x y^{3})}^{2} {(x y)}^{6}$ $(3xy^3)^2(xy)^6$ ?

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How do you simplify ${(3 x y^{3})}^{2} {(x y)}^{6}$ $(3xy^3)^2(xy)^6$ ?

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Answer 1 · 2018-05-04T01:50:39

$9 x^{8} y^{12}$ $9x^8y^12$

Explanation:

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

This can also be written (for simplicity of understanding) as:

${(3^{1} x^{1} y^{3})}^{2} {(x^{1} y^{1})}^{6}$ $(3^1x^1y^3)^2(x^1y^1)^6$

We first open the brackets separately and simplify them by multiplying the exponential power outside the bracket with each individual power inside the bracket.

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

Since $3^{2}$ $3^2$ is $9$ $9$ we write that:

$(9 x^{2} y^{6}) (x^{6} y^{6})$ $(9x^2y^6)(x^6y^6)$

Now we combine both brackets by opening them and multiplying the like terms with each other by adding their respective powers:

$9 x^{8} y^{12}$ $9x^8y^12$

Answer 2 · 2018-05-04T01:51:46

${(3 x y^{3})}^{2} {(x y)}^{6} = 9 x^{8} y^{12}$ $(3xy^3)^2(xy)^6=color(blue)(9x^8y^12$

Explanation:

Simplify:

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

Apply multiplication distributive property: ${(a b)}^{m} = a^{m} b^{m}$ $(ab)^m=a^mb^m$

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

Apply power rule of exponents: ${(a^{m})}^{n} = a^{m \cdot n}$ $(a^m)^n=a^(m*n)$

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

Simplify $3^{2}$ $3^2$ to $9$ $9$ .

$9 x^{2} y^{3 \cdot 2} x^{6} y^{6}$ $9x^2y^(3*2)x^6y^6$

Simplify $y^{3 \cdot 2}$ $y^(3*2)$ to $y^{6}$ $y^6$ .

$9 x^{2} y^{6} x^{6} y^{6}$ $9x^2y^6x^6y^6$

Regroup variables.

$9 x^{2} x^{6} y^{6} y^{6}$ $9x^2x^6y^6y^6$

Apply product rule of exponents: $a^{m} a^{n} = a^{m + n}$ $a^ma^n=a^(m+n)$

$9 x^{2 + 6} y^{6 + 6}$ $9x^(2+6)y^(6+6)$

$9 x^{8} y^{12}$ $9x^8y^12$

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How do you simplify ${(3 x y^{3})}^{2} {(x y)}^{6}$ $(3xy^3)^2(xy)^6$ ?

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How do you simplify ${(3 x y^{3})}^{2} {(x y)}^{6}$ $(3xy^3)^2(xy)^6$ ?