Answer
$\frac{1}{10^{54}}$
Work Step by Step
$(\frac{10^{-7}\times10^{-2}}{10^9})^{-3}$ to multiply powers of 10 add the exponents
$=(\frac{10^{-7+(-2)}}{10^9})^{-3}$
$=(\frac{10^{-9}}{10^9})^{-3}2$ to divide powers of 10, subtract the exponents
$=(10^{-9-9)})^{-3}$
$=(10^{-18})^{-3}\longrightarrow$ to raise a power to a power multiply the exponents
$=10^{-54}$
$=\frac{1}{10^{54}}$