All of the following expressions are equivalent to 3⋅12^t. However, only one has been rewritten using exponent property #3, b^x/b^y = b^(x−y)
Which one is it?
a) 3^(t+1)20^t/5^t
b) 3^(t+1)4^t
c) 3^(t+1)2^2t
d)3⋅12^(t+2)/12^2
only d has 3⋅12^(something)
To find the expression that has been rewritten using exponent property #3, b^x/b^y = b^(x−y), you need to compare the given expressions to 3⋅12^t.
Let's break down each answer choice and simplify them to see which one matches the given property.
a) 3^(t+1)20^t/5^t
To simplify this expression, we can start by using exponent property #3: b^x/b^y = b^(x−y).
For the numerator, we have 3^(t+1) and 20^t, and for the denominator, we have 5^t.
3^(t+1) can be rewritten as 3^t * 3^1 = 3^t * 3.
So the expression becomes:
(3^t * 3) * 20^t / 5^t
Now, we have 3^t in both the numerator and denominator, which cancels out.
The simplified expression becomes 3 * 20^t / 5^t.
b) 3^(t+1)4^t
This expression doesn't require the use of the exponent property since it is already in the form 3⋅12^t.
c) 3^(t+1)2^2t
Similar to the previous expression, this one doesn't require the exponent property because it is already in the desired form.
d) 3⋅12^(t+2)/12^2
Let's simplify this expression by using the exponent property.
First, we have 3⋅12^(t+2). We can rewrite 12^(t+2) as 12^t * 12^2.
So the expression becomes:
3 * (12^t * 12^2) / 12^2
Now, we have 12^2 in both the numerator and denominator, which cancels out.
The simplified expression becomes 3 * 12^t.
After comparing the simplified expressions to 3⋅12^t, we can see that the only one that matches the given exponent property is option d) 3⋅12^(t+2)/12^2.
Therefore, the correct answer is d) 3⋅12^(t+2)/12^2.