Question

Which can be used to describe an equivalent expression for (s Superscript 6 Baseline) Superscript negative 3?


Adding the exponents will create an equivalent expression.
Dividing the exponents will create an equivalent expression.
There are three factors of StartFraction 1 Over s Superscript 6 Baseline EndFraction.
There are three factors of StartFraction 1 Over s Superscript 3 Baseline EndFraction.

Answer 1

Only the third statement is correct.

Reason: (s^6)^(-3) = s^{6·(-3)} = s^{-18} = 1/s^{18}. That equals (1/s^6)^3, so it is three factors of 1/s^6.

Adding or dividing exponents is incorrect (adding exponents applies when multiplying like bases; dividing when dividing like bases). The fourth option gives (1/s^3)^3 = 1/s^9, not equal to s^{-18}.