Simplifying Exponential Expressions
To simplify the expression \(\frac{2^{n+1}}{2^n * 2}\), you can use the properties of exponents.
Here is how you can simplify it step by step:
1. The expression \(\frac{2^{n+1}}{2^n * 2}\) can be rewritten by separating the terms in the denominator, so you have \(\frac{2^{n+1}}{2^n \cdot 2^1}\).
2. Now you can apply the quotient rule for exponents, which states that when dividing like bases, you subtract the exponents: \(\frac{2^{n+1}}{2^n}\) becomes \(2^{(n+1)-n} = 2^1 = 2\).
3. So now you have \(2 \div 2^1\).
4. Applying the division rule for exponents again (or recognizing that any number divided by itself is 1), you have \(2^1 \div 2^1 = 2^{1-1} = 2^0 = 1\).
The simplified form of the expression is \(1\).
