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

`3^(-3)\cdot \:\:8^(-3)=(1)/(24^3)`

Thus, the equivalent expression is:
`(1)/(24^3)`

Explanation:

Given the expression

`3^(-3)\cdot 8^(-3)`

`\mathrm{Apply\:exponent\:rule}:\quad \:a^(-b)=(1)/(a^b)`

`=8^(-3)\cdot (1)/(3^3)`

`\mathrm{Apply\:exponent\:rule}:\quad \:a^(-b)=(1)/(a^b)`

`=(1)/(3^3)\cdot (1)/(8^3)`

`\mathrm{Multiply\:fractions}:\quad (a)/(b)\cdot (c)/(d)=(a\:\cdot \:c)/(b\:\cdot \:d)`

`=(1\cdot \:1)/(3^3\cdot \:8^3)`

`=(1)/(24^3)`

Thus,

`3^(-3)\cdot \:\:8^(-3)=(1)/(24^3)`

Thus, the equivalent expression is:
`(1)/(24^3)`