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
The equivalent expression for 5 1/2 / 125√3 when simplified using exponent properties is √5/5.
To simplify the expression 5 1/2 / 125√3 using exponent properties, we can rewrite the terms with fractional exponents and simplify.
First, let's consider 5^(1/2). This means we need to find the square root of 5.
Next, let's consider 125√3. We can rewrite this as 125^(1/3) * 3^(1/2).
Now, we can simplify the expression:
5^(1/2) / (125^(1/3) * 3^(1/2))
Since 5^(1/2) is the square root of 5, we can rewrite it as √5.
√5 / (125^(1/3) * 3^(1/2))
Now, let's simplify the remaining terms.
125^(1/3) is the cube root of 125, which is 5.
3^(1/2) is the square root of 3.
So, the expression becomes:
√5 / (5 * √3)
We can simplify this expression further by dividing both the numerator and denominator by 5:
(√5/5) / (√3)
Therefore, the equivalent expression for 5 1/2 / 125√3 when simplified using exponent properties is √5/5.