Question

Simplify b^3 × b^-3 for b = 5.

Answer 1

b^3 is the same as b * b *b
b^-3 is the same as 1/b^3 = 1/b * 1/b * 1/b

so what you have is: \[(b * b * b) * (\frac{ 1 }{ b } * \frac{ 1 }{ b } * \frac{ 1 }{ b} )\]
which is the same as \[\frac{ b * b * b }{ b * b*b} \] all of the b's cancel out to become 1 regardless of what value b is: Example: \[\frac{ 5 * 5 * 5 }{ 5 * 5 * 5 } = \frac{ 125 }{ 125 } = 1\]

Answer 2

Thank you :)