Which expression or expressions are equivalent to 3^n/2^n?
3^n/2^n = (3/2)^n
To find equivalent expressions for the given expression 3^n/2^n, we can use the properties of exponents.
First, we can simplify the expression by dividing the coefficients:
3^n/2^n = (3/2)^n
Now, let's break it down further into multiple equivalent expressions:
1. (3/2)^n - This is the simplified form of the given expression.
2. 1.5^n - When we substitute 3/2 with its decimal form 1.5.
3. (√3/√2)^n - We can rewrite 3/2 as (√3/√2) using the square root property.
4. (√3)^n / (√2)^n - We can split the numerator and denominator into separate exponents.
These are some equivalent expressions for 3^n/2^n.
To determine which expression(s) are equivalent to 3^n/2^n, let's break down the problem step by step.
First, let's rewrite the given expression:
3^n/2^n
Since both the numerator and denominator have the same base of 2, we can rewrite this expression using the exponent rule:
(3/2)^n
Now we have (3/2) raised to the power of n.
To find the equivalent expression(s), we need to consider the different properties of exponents and their simplified forms.
Here are some possible equivalent expressions:
1) (3/2)^n
2) (3/2)^n = (3^1/2^1)^n = (3/2)^n
3) 3^n/2^n = (3/2)^n
Therefore, the expression (3/2)^n is equivalent to 3^n/2^n.