Question

question 22 of 40
simplify the expression. write the answer with positive exponents on
$y^{\frac{3}{7}} y^{\frac{8}{3}}$
$y^{\frac{3}{7}} y^{\frac{8}{3}} = \underline{\quad\quad}$

Explanation:

Step1: Apply exponent product rule

When multiplying exponential expressions with the same base, we add the exponents: \(a^m \cdot a^n = a^{m + n}\). Here, the base is \(y\), so \(y^{\frac{3}{7}} \cdot y^{\frac{8}{3}} = y^{\frac{3}{7}+\frac{8}{3}}\).

Step2: Add the fractions

Find a common denominator for \(\frac{3}{7}\) and \(\frac{8}{3}\), which is \(21\). Convert the fractions: \(\frac{3}{7}=\frac{3\times3}{7\times3}=\frac{9}{21}\) and \(\frac{8}{3}=\frac{8\times7}{3\times7}=\frac{56}{21}\). Then add them: \(\frac{9}{21}+\frac{56}{21}=\frac{9 + 56}{21}=\frac{65}{21}\). So the expression simplifies to \(y^{\frac{65}{21}}\).

Answer:

\(y^{\frac{65}{21}}\)