Question

Which expression is equivalent to 32 ⋅ 3−5? fraction 1 over 3 to the power 3 fraction 1 over 3 to the power 7 fraction 1 over 3 to the power negative 3 fraction 1 over 3 to the power negative 7?

Answer 1

Given expression 3² × 3⁻⁵

We will apply the power rule
`x^m*x^n=x^(m+n)`

3² × 3⁻⁵ = 3²⁺⁽⁻⁵⁾ = 3²⁻⁵ = 3⁻³

We will then apply the power rule
`x^(-n) = (1)/(x^n)`

3⁻³ =
`(1)/(3^3)`

Final answer:
`(1)/(3^3)`