Full simplify (y4y2)3⋅(y9y6)4\left(\frac{y^{4}}{y^{2}}\right)^{3}\cdot\left(\frac{y^{9}}{y^{6}}\right)^{4}(

Question

y
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Answer 1

To simplify the expression \(\left(\frac{y^{4}}{y^{2}}\right)^{3}\cdot\left(\frac{y^{9}}{y^{6}}\right)^{4}\), we can follow these steps:

Step 1: Simplify Each Fraction

1. For the first fraction: \[ \frac{y^{4}}{y^{2}} = y^{4-2} = y^{2} \] Therefore: \[ \left(\frac{y^{4}}{y^{2}}\right)^{3} = (y^{2})^{3} = y^{2 \times 3} = y^{6} \]

2. For the second fraction: \[ \frac{y^{9}}{y^{6}} = y^{9-6} = y^{3} \] Therefore: \[ \left(\frac{y^{9}}{y^{6}}\right)^{4} = (y^{3})^{4} = y^{3 \times 4} = y^{12} \]

Step 2: Multiply the Results

Now, we can combine the results: \[ y^{6} \cdot y^{12} \]

Step 3: Use the Property of Exponents

When we multiply exponents with the same base, we add the exponents: \[ y^{6 + 12} = y^{18} \]

Final Result

Thus, the final simplified expression is: \[ \boxed{y^{18}} \]