All of the following expressions are equal to 1/10⋅20^t. However, only one has been rearranged by applying the exponent property that states b^x/b^y=b^x−y.
a)(1/10) ⋅ 5^t ⋅ 4^t
b)(1/10) ⋅ 10^t ⋅ 2^t
c) 2^(2t-1) ⋅ 5^(t-1)
d) (1/10) ⋅ (2^2t) ⋅ (5^t)
You mean b^x/b^y=b^(x−y) parentheses matter
2^(2t-1) ⋅ 5^(t-1)
= 2^2t / 2^1 * 5^t /5^1
= 4^t/2 * 5^t/5
= 20^t / 10
but 4^t * 5^t = 20^t does not illustrate the named property.
It illustrates a^t * b^t = (ab)^t
There have been several of these posts, and almost all of them have been very poorly presented.
To determine which expression has been rearranged using the exponent property, we need to simplify each expression and see if any of them match the form b^x/b^y = b^(x-y).
Let's simplify each expression:
a) (1/10) ⋅ 5^t ⋅ 4^t = (1/10) ⋅ (5 ⋅ 4)^t = (1/10) ⋅ (20)^t = 1/10 ⋅ 20^t
b) (1/10) ⋅ 10^t ⋅ 2^t = (1/10) ⋅ (10 ⋅ 2)^t = (1/10) ⋅ (20)^t = 1/10 ⋅ 20^t
c) 2^(2t-1) ⋅ 5^(t-1)
d) (1/10) ⋅ (2^2t) ⋅ (5^t) = (1/10) ⋅ (2^t ⋅ 2^t) ⋅ (5^t) = (1/10) ⋅ (2^t ⋅ 2^t) ⋅ (5^t) = (1/10) ⋅ (2^t ⋅ 2^t) ⋅ (5^t) = (1/10) ⋅ 2^(2t) ⋅ (5^t)
Comparing the simplified expressions, we can see that both expression a) and expression b) match the form b^x/b^y = b^(x-y) with b = 20, x = t, and y = 0.
Therefore, the rearranged expression using the exponent property is a) and b), i.e., both expressions (1/10) ⋅ 5^t ⋅ 4^t and (1/10) ⋅ 10^t ⋅ 2^t are equal to 1/10 ⋅ 20^t after applying the exponent property.