Solution:
Given the expression:
[tex](-5p^6\cdot r^{-9})^0[/tex]
Simplifying using the law of exponents,
[tex]\begin{gathered} (-5p^6\cdot r^{-9})^0=(-5\times p^{-6}\times r^{-9})^0 \\ \end{gathered}[/tex]
but
[tex]a^{-b}=\frac{1}{a^b}[/tex]
thus, we have
[tex]\begin{gathered} (-5\times p^{-6}\times r^{-9})^0=(-5\times\frac{1}{p^6}\times\frac{1}{r^9})^0 \\ =(-\frac{5}{p^6r^9})^0 \end{gathered}[/tex]
From the zero index law of exponents,
[tex]a^0=1[/tex]
This implies that
[tex](-\frac{5}{p^6r^9})^0=1[/tex]
Hence, the solution to the expression is 1
