How do you simplify $\frac{{[2 a^{4} b]}^{3}}{24 b^{5}}$ $[2a^4b]^3/(24b^5)$ ?

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Answer 1 · 2015-06-15T16:43:58

Expand the numerator then (by grouping) simplify the fraction to get
$\frac{a^{12}}{3 b^{2}}$ $(a^12)/(3b^2)$

$\frac{{[2 a^{4} b]}^{3}}{24 b^{5}}$ $([2a^4b]^3) / (24b^5)$

$= \frac{8 a^{12} b^{3}}{24 b^{5}}$ $= (8a^12b^3) / (24b^5)$

$= (\frac{8}{24}) \cdot (\frac{a^{12}}{1}) \cdot (\frac{b^{3}}{b^{5}})$ $= (8/24) * ((a^12)/1) * ((b^3)/(b^5))$

$= (\frac{1}{3}) \cdot (\frac{a^{12}}{1}) \cdot (\frac{1}{b^{2}})$ $= (1/3) * ((a^12)/1) * (1/(b^2))$

$= \frac{a^{12}}{3 b^{2}}$ $= (a^12)/(3b^2)$

How do you simplify [2a^4b]^3/(24b^5)[2a4b]324b5[2a^4b]^3/(24b^5)?