Yes, $y^{\frac{7}{4}}$ is equal to $y \cdot y^{\frac{3}{4}}$.

This equality holds because of the properties of exponents. Specifically:

$y^{\frac{7}{4}} = y^{\frac{4}{4} + \frac{3}{4}} = y^{\frac{4}{4}} \cdot y^{\frac{3}{4}} = y \cdot y^{\frac{3}{4}}$

So, the two expressions are indeed equivalent.

Would you like more details on this, or do you have any other questions?

Here are 8 related questions you might find interesting:

1. How do you split a fractional exponent into a sum of two fractions?
2. What are the rules for multiplying terms with the same base?
3. How do you simplify expressions involving multiple terms with fractional exponents?
4. Can you always break down exponents in this way for any exponent value?
5. How would you expand $y^{\frac{7}{4}}$ into a product of three or more terms?
6. What is the inverse operation of multiplying terms with the same base?
7. How do fractional exponents relate to radical expressions?
8. How can you apply this property to solve equations involving fractional exponents?

Tip: When working with exponents, remember that adding exponents corresponds to multiplying the bases. This principle is key when simplifying expressions or solving equations involving powers.