is 8^-3 equivalent to 1/3^8

Answer 1

Yes, 8^-3 is equivalent to 1/3^8.

To see this, we can rewrite 8^-3 as (2^3)^-3. Using the power of a power property, this simplifies to 2^(3*-3) which is equal to 2^-9.

Similarly, we can rewrite 1/3^8 as 3^-8 by using the reciprocal property.

Since 2^-9 is equal to 1/2^9 and 1/2^9 is equal to 1/(2^3)^3, which is equal to 1/8^3, we can conclude that 2^-9 is equivalent to 1/3^8.