Question

simplify.
$y^{\frac{1}{2}} \cdot y^{\frac{5}{8}}$
assume that the variable represents a positive real number.

Explanation:

Step1: Recall exponent rule for multiplication

When multiplying two exponential expressions with the same base, we add the exponents: \(a^m \cdot a^n = a^{m + n}\). Here, the base is \(y\), so we add the exponents \(\frac{1}{2}\) and \(\frac{5}{8}\).

Step2: Find a common denominator and add exponents

The common denominator of 2 and 8 is 8. Convert \(\frac{1}{2}\) to eighths: \(\frac{1}{2}=\frac{4}{8}\). Now add the exponents: \(\frac{4}{8}+\frac{5}{8}=\frac{4 + 5}{8}=\frac{9}{8}\). So the simplified form is \(y^{\frac{9}{8}}\).

Answer:

\(y^{\frac{9}{8}}\)