A fraction reduces to 36. If its denominator is 6x^5, what is its numerator?
a. 6^3x
b. 6^3x^5
c. 6x^5
d. 6^7x^5
To reduce a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both the numerator and the denominator by this GCD.
In this case, we are told that the fraction reduces to 36 and its denominator is 6x^5.
To find the GCD of the numerator and denominator, let's express both in prime factorization form.
We can express 36 as 2^2 * 3^2.
We can express 6x^5 as 2^1 * 3^1 * x^5.
The GCD of the numerator and denominator is the product of the common prime factors with the lowest exponents, which is 2^1 * 3^1 = 6.
To reduce the fraction, we divide both the numerator and denominator by this GCD:
Numerator = (2^2 * 3^2) / (2^1 * 3^1 * x^5)
= (2^1 * 3^1) / (x^5)
= 6 / (x^5)
Therefore, the numerator is 6, and the answer is option: c. 6x^5.