Question

Can you help me with this math problem? Im having a hard time with it, if you can explain it too that would help a lot. attachment below

Answer 1

Answer:

$3^{-3}\cdot \:\:8^{-3}=\frac{1}{24^3}$

Thus, the equivalent expression is:  $\frac{1}{24^3}$

Step-by-step explanation:

Given the expression

$3^{-3}\cdot 8^{-3}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

$=8^{-3}\cdot \frac{1}{3^3}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

$=\frac{1}{3^3}\cdot \frac{1}{8^3}$

$\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}$

$=\frac{1\cdot \:1}{3^3\cdot \:8^3}$

$=\frac{1}{24^3}$

Thus,

$3^{-3}\cdot \:\:8^{-3}=\frac{1}{24^3}$

Thus, the equivalent expression is:  $\frac{1}{24^3}$