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  4. ((ap+q)15 ⋅(aq+r)15 ⋅(ar+p)15/(ap+q+r)29)=

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Q. $ \frac{\left(a^{p+q}\right)^{15} \cdot\left(a^{q+r}\right)^{15} \cdot\left(a^{r+p}\right)^{15}}{\left(a^{p+q+r}\right)^{29}}= $___

Squares and Square Roots and Cubes and Cube Roots

Solution:

$ \frac{\left(a^{p+q}\right)^{15}\left(a^{q+r}\right)^{15}\left(a^{r+p}\right)^{15}}{\left(a^{p+q+r}\right)^{29}}$
$=\frac{\left(a^{p+q+q+r+r+p}\right)^{15}}{\left(a^{p+q+r}\right)^{29}}$
$= \frac{\left(a^{p+q+r}\right)^{30}}{\left(a^{p+q+r}\right)^{29}} $
$= a^{p+q+r}$