Question
Fully simplify (y^-5*y^4)^5
Answers
GPT-4o mini
Let's break down the expression \((y^{-5} y^{4})^{5}\).
1. **Combine the exponents inside the parentheses**: When multiplying like bases, we add the exponents:
\[
y^{-5} y^{4} = y^{-5 + 4} = y^{-1}
\]
2. **Now raise the result to the power of 5**:
\[
(y^{-1})^{5} = y^{-1 \cdot 5} = y^{-5}
\]
3. **Convert negative exponent to positive**:
\[
y^{-5} = \frac{1}{y^{5}}
\]
So, the fully simplified expression is:
\[
\frac{1}{y^{5}}
\]
1. **Combine the exponents inside the parentheses**: When multiplying like bases, we add the exponents:
\[
y^{-5} y^{4} = y^{-5 + 4} = y^{-1}
\]
2. **Now raise the result to the power of 5**:
\[
(y^{-1})^{5} = y^{-1 \cdot 5} = y^{-5}
\]
3. **Convert negative exponent to positive**:
\[
y^{-5} = \frac{1}{y^{5}}
\]
So, the fully simplified expression is:
\[
\frac{1}{y^{5}}
\]