Answer:
We conclude that
[tex]3^{-3}\times \:8^{-6}=\frac{1}{8^6\times \:\:3^3}[/tex]
Step-by-step explanation:
Given the expression
[tex]3^{-3}\times \:8^{-6}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}[/tex]
[tex]3^{-3}\times\:8^{-6}=8^{-6}\times \:\frac{1}{3^3}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}[/tex]
[tex]=\frac{1}{3^3}\times \frac{1}{8^6}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]
[tex]=\frac{1\times \:1}{3^3\times \:8^6}[/tex]
[tex]=\frac{1}{8^6\times \:3^3}[/tex]
Therefore, we conclude that
[tex]3^{-3}\times \:8^{-6}=\frac{1}{8^6\times \:\:3^3}[/tex]
