Full simplify (𝑦5𝑦3)3⋅(𝑦7𝑦4)5\left(\frac{y^{5}}{y^{3}}\right)^{3}\cdot\left(\frac{y^{7}}{y^{4}}\right)^{5}( y 3 y 5 ​ ) 3 ⋅( y 4 y 7 ​ ) 5

Answer 1

To simplify the expression \(\left(\frac{y^{5}}{y^{3}}\right)^{3}\cdot\left(\frac{y^{7}}{y^{4}}\right)^{5}\), we can follow these steps:

1. Simplify each fraction:

   • \(\frac{y^{5}}{y^{3}} = y^{5-3} = y^{2}\)
   • \(\frac{y^{7}}{y^{4}} = y^{7-4} = y^{3}\)

2. Substitute back into the original expression: \[ \left(y^{2}\right)^{3} \cdot \left(y^{3}\right)^{5} \]

3. Apply the power of a power rule:

   • \(\left(y^{2}\right)^{3} = y^{2 \cdot 3} = y^{6}\)
   • \(\left(y^{3}\right)^{5} = y^{3 \cdot 5} = y^{15}\)

4. Multiply the results: \[ y^{6} \cdot y^{15} = y^{6 + 15} = y^{21} \]

Thus, the fully simplified expression is:

\[ \boxed{y^{21}} \]