To find the least common denominator (LCD) of the fractions [tex]\(\frac{35}{y^4}\)[/tex] and [tex]\(\frac{175}{y^8}\)[/tex], we need to follow these steps:
1. Identify the denominators of the given fractions.
For [tex]\(\frac{35}{y^4}\)[/tex], the denominator is [tex]\(y^4\)[/tex].
For [tex]\(\frac{175}{y^8}\)[/tex], the denominator is [tex]\(y^8\)[/tex].
2. Compare the two denominators to find the least common multiple (LCM) of the powers of [tex]\(y\)[/tex].
We are dealing with [tex]\(y^4\)[/tex] and [tex]\(y^8\)[/tex].
Recall that when finding the LCM of terms with the same base but different exponents, we take the base with the highest exponent.
Here, [tex]\(y^4\)[/tex] and [tex]\(y^8\)[/tex] have the base [tex]\(y\)[/tex]. The exponents are 4 and 8, respectively. The higher exponent is 8.
3. Determine the least common denominator by taking the base [tex]\(y\)[/tex] with the highest exponent found in step 2.
Therefore, the least common denominator of [tex]\(\frac{35}{y^4}\)[/tex] and [tex]\(\frac{175}{y^8}\)[/tex] is [tex]\(y^8\)[/tex].
Thus, the least common denominator (LCD) of the fractions [tex]\(\frac{35}{y^4}\)[/tex] and [tex]\(\frac{175}{y^8}\)[/tex] is [tex]\(y^8\)[/tex].
