How do you simplify ${(\frac{3 x^{7}}{2})}^{6} {(x^{2})}^{6}$ $((3x^7)/2)^6(x^2)^6$ ?

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How do you simplify ${(\frac{3 x^{7}}{2})}^{6} {(x^{2})}^{6}$ $((3x^7)/2)^6(x^2)^6$ ?

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Answer 1 · 2018-06-20T11:22:22

$\Rightarrow (\frac{729}{64}) x^{54}$ $color(purple)(=> (729/64)x^54$

Explanation:

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

$a^{m} \cdot a^{n} = a^{m + n}, {(a^{m})}^{n} = a^{m n}$ $a^m * a^n = a^(m + n), (a^m)^n = a^(mn)$

${(\frac{3 x^{7}}{2})}^{6} \cdot {(x^{2})}^{6}$ $((3x^7)/2)^6 * (x^2)^6$

$\Rightarrow {((\frac{3 x^{7}}{2}) \cdot x^{2})}^{6}$ $=> (((3x^7) / 2)* x^2)^6$

$\Rightarrow {(\frac{3 x^{9}}{2})}^{6}$ $=> ((3x^9)/2)^6$

$\Rightarrow \frac{3^{6} \cdot x^{9 \cdot 6}}{2^{6}}$ $=> (3^6 * x^(9*6)) / 2^6$

$\Rightarrow (\frac{729}{64}) x^{54}$ $color(purple)(=> (729/64)x^54$

Answer 2 · 2018-06-20T11:24:13

$\frac{729}{64} x^{54}$ $729/64 x^54$

Explanation:

In general $a^{p} \cdot b^{p} = {(a \cdot b)}^{p}$ $color(red)a^color(lime)p * color(blue)b^color(lime)p=(color(red)a * color(blue)b)^color(lime)p$

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

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

$XXX = \frac{3^{6}}{2^{6}} x^{9 \cdot 6}$ $color(white)("XXX")=(3^6)/(2^6) x^(9 * 6)$

$XXX = \frac{729}{64} x^{54}$ $color(white)("XXX")=729/64 x^54$

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2 Answers

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