Use the properties of exponents to simplify the expression so that only positive exponents remain.

Question

Use the properties of exponents to simplify the expression so that only positive exponents remain. ​  ​

Quizplus · Accepted Answer

The property of exponents states that x^(-n) is equivalent to 1/(x^n). Applying this property to the negative exponent in the expression, we get 1/(e^(-2b)+e^(-b)). We can then use the property that (a+b)^(-1) is equivalent to 1/(a+b) to simplify further, giving us 1/[(e^(-b))(e^(-b)+1)]. Finally, we use the property that e^(-b) is equivalent to 1/(e^b) to substitute and simplify to get the expression in Choice B: (e^b)/(1+e^b).

Use the Properties of Exponents to Simplify the Expression So