Which of the following is an equivalent expression for 5^1/2/125√3 when simplified using exponent properties?(1 point)
Responses
50
5 superscript 0 baseline
1
1
15
Start Fraction 1 over 5 End Fraction
5√5
The correct answer is 5√5.
To simplify the expression 5^(1/2) / (125√3), you can first simplify the numerator. The exponent 1/2 represents the square root of 5.
So, 5^(1/2) = √5
Now, you have:
√5 / (125√3)
To simplify further, you can simplify the denominator by breaking down 125 into its prime factors.
125 = 5 * 5 * 5
So, you have:
√5 / (5 * 5 * 5√3)
Now, you can cancel out one factor of 5 in the denominator with the square root of 5 in the numerator:
√5 / (5 * 5√3)
And simplifying further:
√5 / (25√3)
Finally, to simplify the expression completely, you can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator, which is √3.
(√5 * √3) / (25√3 * √3)
Simplifying:
(√15) / (25 * 3)
= (√15) / 75
Therefore, the equivalent expression for 5^(1/2) / (125√3) when simplified using exponent properties is (√15) / 75.