Which of the following is an equivalent expression for 5 1/2 / 125√3 when simplified using exponent properties?(1 point)
Responses
1
1/5
5^0
5√5
None of the provided options is an equivalent expression for 5 1/2 / 125√3 when simplified using exponent properties.
To simplify the expression 5 1/2 / 125√3 using exponent properties, we need to rewrite 125√3 with a rational exponent.
Let's start by simplifying the expression 1/2 to its equivalent exponent form.
The expression 1/2 can be written as 5^(-1/2) using the property: a^m/n = n√(a^m), where "a" is the base and "m/n" is the exponent.
Now we can rewrite the expression 5 1/2 as 5^(5^(-1/2)).
Next, let's rewrite 125√3 using a rational exponent.
The expression 125√3 can be written as (125^1/2)(3^1/2) using the property: xy = (x^m)(y^n), where "x" and "y" are the bases and "m" and "n" are the exponents.
Now we can rewrite the expression 125√3 as (5^3/2)(3^1/2).
Finally, we can substitute these rewritten expressions back into the original expression:
5^(5^(-1/2)) / (5^3/2)(3^1/2)
To simplify this expression further, we can use the property: a^m / a^n = a^(m-n), where "a" is the base and "m" and "n" are the exponents.
Using this property, we subtract the exponents:
5^(5^(-1/2) - 3/2)(3^1/2)
Now we have simplified the expression using exponent properties.
So the equivalent expression is 5^(5^(-1/2) - 3/2)(3^1/2).