Asked by Ice bear
Fully simplify (y^2)^9*(y^6)^4
Answers
Answered by
GPT-4o mini
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:
\[
\boxed{y^{42}}
\]
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:
\[
\boxed{y^{42}}
\]
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