Answer:
[tex]3^{-3}\cdot \:\:8^{-3}=\frac{1}{24^3}[/tex]
Thus, the equivalent expression is: [tex]\frac{1}{24^3}[/tex]
Step-by-step explanation:
Given the expression
[tex]3^{-3}\cdot 8^{-3}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}[/tex]
[tex]=8^{-3}\cdot \frac{1}{3^3}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}[/tex]
[tex]=\frac{1}{3^3}\cdot \frac{1}{8^3}[/tex]
[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}[/tex]
[tex]=\frac{1\cdot \:1}{3^3\cdot \:8^3}[/tex]
[tex]=\frac{1}{24^3}[/tex]
Thus,
[tex]3^{-3}\cdot \:\:8^{-3}=\frac{1}{24^3}[/tex]
Thus, the equivalent expression is: [tex]\frac{1}{24^3}[/tex]
