All of the following expressions are equivalent to 7⋅(2/10)^t. However, only one has been rewritten using exponent property #4, (b/c)^x = b^x/c^x.
Which one is it?
a) (71^(t/5)/5)^t
b) 7⋅(1/5)^t
c) (7^(1/t)⋅2/10)^t
d) 7⋅2^t/10^t
To identify the expression that has been rewritten using exponent property #4, we need to compare each option to the original expression, which is 7⋅(2/10)^t.
Exponent property #4 states that (b/c)^x = b^x / c^x. This property allows us to separate the numerator and denominator of a fraction raised to a power.
Let's analyze each option to see if it matches the rewritten expression using this property:
a) (71^(t/5)/5)^t: This expression has a different base (71) and additional terms (5) in both the numerator and denominator. It does not match with the rewritten expression.
b) 7⋅(1/5)^t: This option matches the rewritten expression using exponent property #4. The original expression has (2/10)^t, and this option has (1/5)^t. By substituting 2 with 1 and 10 with 5 in the original expression, we get this option.
c) (7^(1/t)⋅2/10)^t: This expression has additional factors (7^(1/t) and 2) in the numerator. It does not match with the rewritten expression.
d) 7⋅2^t/10^t: This expression has the same factors (7, 2, and 10) as the original expression, but it does not separate the numerator and denominator like the rewritten expression using exponent property #4. It does not match with the rewritten expression.
Therefore, the expression that has been rewritten using exponent property #4 is b) 7⋅(1/5)^t.