Question
Fully simplify (y−5⋅y7)4\left(y^{-5}\cdot y^{7}\right)^{4}(y
−5
⋅y
7
)
4
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Answers
GPT-4o mini
To simplify the expression \((y^{-5} \cdot y^{7})^{4}\), we can follow these steps:
1. **Combine the terms inside the parentheses:** Since we have the same base \(y\), we can add the exponents:
\[
y^{-5} \cdot y^{7} = y^{-5 + 7} = y^{2}
\]
2. **Now raise the result to the power of 4:** We apply the exponent to \(y^{2}\):
\[
(y^{2})^{4} = y^{2 \cdot 4} = y^{8}
\]
Putting it all together, the fully simplified form of \((y^{-5} \cdot y^{7})^{4}\) is:
\[
\boxed{y^{8}}
\]
1. **Combine the terms inside the parentheses:** Since we have the same base \(y\), we can add the exponents:
\[
y^{-5} \cdot y^{7} = y^{-5 + 7} = y^{2}
\]
2. **Now raise the result to the power of 4:** We apply the exponent to \(y^{2}\):
\[
(y^{2})^{4} = y^{2 \cdot 4} = y^{8}
\]
Putting it all together, the fully simplified form of \((y^{-5} \cdot y^{7})^{4}\) is:
\[
\boxed{y^{8}}
\]