Question

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:

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