Answer:
The given expression [tex](\frac{5}{6} a^{9}p^{5}) ^{3} = \frac{125}{216} \times a^{(27) } \times p^{(15)}[/tex]
Step-by-step explanation:
Here, the given expression is: [tex](\frac{5}{6} a^{9}p^{5}) ^{3}[/tex]
Now, starting from the outer most bracket.
As we know :
[tex](abc)^{n} = (a)^{n} \times (b)^{n} \times (c)^{n}[/tex]
and [tex](a^m)^{n} = a^{(m \times n)}[/tex]
⇒ [tex](\frac{5}{6} a^{9}p^{5}) ^{3} = (\frac{5}{6})^{3} \times (a^{9})^{3} \times (p^{5}) ^{3}\\[/tex]
[tex]=\frac{125}{216} \times (a)^{(9\times3) } \times (p)^{(5 \times 3)}\\= \frac{125}{216} \times a^{(27) } \times p^{(15)}[/tex]
Hence, the given expression [tex](\frac{5}{6} a^{9}p^{5}) ^{3} = \frac{125}{216} \times a^{(27) } \times p^{(15)}[/tex]
