How do you simplify $((3x^7)/2)^6(x^2)^6$ ?

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How do you simplify $((3x^7)/2)^6(x^2)^6$ ?

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Answer 1 · 2018-06-20T11:22:22

$color(purple)(=> (729/64)x^54$

Explanation:

![https://revisionmaths.com/advanced-level-maths-revision/pure-maths/algebra/indices]( useruploads.socratic.org )

$a^m * a^n = a^(m + n), (a^m)^n = a^(mn)$

$((3x^7)/2)^6 * (x^2)^6$

$=> (((3x^7) / 2)* x^2)^6$

$=> ((3x^9)/2)^6$

$=> (3^6 * x^(9*6)) / 2^6$

$color(purple)(=> (729/64)x^54$

Answer 2 · 2018-06-20T11:24:13

$729/64 x^54$

Explanation:

In general $color(red)a^color(lime)p * color(blue)b^color(lime)p=(color(red)a * color(blue)b)^color(lime)p$

So
$color(white)("XXX")(color(red)((3x^7)/2))^color(lime)6 (color(blue)(x^2))^color(lime)(6)= ((color(red)(3x^7) * color(blue)(x^2))/color(red)2)^color(lime)6$

$color(white)("XXX")=((3x^9)/color(red)2)^color(lime)6$

$color(white)("XXX")=(3^6)/(2^6) x^(9 * 6)$

$color(white)("XXX")=729/64 x^54$

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How do you simplify $((3x^7)/2)^6(x^2)^6$ ?

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How do you simplify ((3x^7)/2)^6(x^2)^6((3x^7)/2)^6(x^2)^6?

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How do you simplify $((3x^7)/2)^6(x^2)^6$ ?