Fully simplify (y^2)^9*(y^6)^4

Answer 1

To simplify \((y^2)^9 \cdot (y^6)^4\), we can use the power of a power property, which states that \((a^m)^n = a^{m \cdot n}\).

1. Apply the power of a power property to \((y^2)^9\) and \((y^6)^4\):

\[ (y^2)^9 = y^{2 \cdot 9} = y^{18} \]

\[ (y^6)^4 = y^{6 \cdot 4} = y^{24} \]

2. Now, we can multiply the two results together:

\[ y^{18} \cdot y^{24} \]

3. When multiplying with the same base, we add the exponents:

\[ y^{18 + 24} = y^{42} \]

The fully simplified expression is:

\[ \boxed{y^{42}} \]