How do you simplify $\frac{{(4 p^{2})}^{8}}{{(4 p^{2})}^{6}}$ $(4p^2)^8 / (4p^2)^6$ ?

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How do you simplify $\frac{{(4 p^{2})}^{8}}{{(4 p^{2})}^{6}}$ $(4p^2)^8 / (4p^2)^6$ ?

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Answer 1 · 2016-03-24T17:32:03

$= 16 p^{4}$ $= 16 p^ (4)$

Explanation:

$\frac{{(4 p^{2})}^{8}}{{(4 p^{2})}^{6}}$ $((4p^2)^8) / ((4p^2)^6)$

By property:
${(a^{m})}^{n} = a^{m n}$ $color(blue)((a^m))^n = a ^(mn)$

$\frac{{(4 p^{2})}^{8}}{{(4 p^{2})}^{6}} = \frac{(4^{8} p^{2 \cdot 8})}{(4^{6} p^{2 \cdot 6})}$ $((4p^2)^8) / ((4p^2)^6)= ((4^8p^(2 * 8 ) )) / ((4^ 6 p^( 2 * 6))$

$= \frac{(4^{8} p^{16})}{(4^{6} p^{12})}$ $= ((4^8p^ 16 )) / ((4^ 6 p^12)$

$= (\frac{4^{8}}{4^{6}}) \cdot \frac{(p^{16})}{(p^{12})}$ $= (4^8 / 4 ^6) * (( p^ 16 )) / ((p^12)$

By property:
$\frac{a^{m}}{a^{n}} = a^{m - n}$ $color(blue)(a^m / a ^n = a ^(m-n)$

$= 4^{(8 - 6) \cdot (p^{16 - 12})}$ $= 4^((8 - 6 ) * ( p^ (16 -12 ))$

$= 4^{2} p^{4}$ $= 4^(2 ) p^ (4)$

$= 16 p^{4}$ $= 16 p^ (4)$

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How do you simplify $\frac{{(4 p^{2})}^{8}}{{(4 p^{2})}^{6}}$ $(4p^2)^8 / (4p^2)^6$ ?

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Explanation:

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How do you simplify (4p^2)^8 / (4p^2)^6 (4p2)8(4p2)6(4p^2)^8 / (4p^2)^6 ?

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How do you simplify $\frac{{(4 p^{2})}^{8}}{{(4 p^{2})}^{6}}$ $(4p^2)^8 / (4p^2)^6$ ?