Answer
$2^x=10$
Work Step by Step
Note that $-3x=x(-3)$.
Thus, $2^{-3x}$ can be written as $2^{x(-3)}$.
RECALL:
(1) $a^{mn} = (a^m)^n$
(2) $a^m = b^m \longrightarrow a=b$
(3) $\dfrac{1}{a^m} = a^{-m}$
Use rule (1) above to obtain:
$2^{x(-3)} = (2^x)^{-3}$
Thus, $2^{-3x}$ in the given equation may be replaced with its equivalent $(2^x)^{-3}$ to obtain:
$(2^x)^{-3} = \dfrac{1}{1000}$
Note that $1000=10^3$, so the expression above is equivalent to:
$(2^x)^{-3} = \dfrac{1}{10^3}$
Use rule (3) above to obtain:
$(2^x)^{-3} = 10^{-3}$
Use rule (2) above to obtain: $2^x=10$
