To simplify the expression \((y^{-4} \cdot y^{7})^{7}\), we can start by using the properties of exponents. 1. **Combine the exponents inside the parentheses:** \[ y^{-4} \cdot y^{7} = y^{-4 + 7} = y^{3} \] 2. **Now simplify the expression raised to the power of 7:** \[ (y^{3})^{7} = y^{3 \cdot 7} = y^{21} \] Therefore, the simplified form of the original expression \((y^{-4} \cdot y^{7})^{7}\) is: \[ \boxed{y^{21}} \]

(y^-4 * y^7)^7

1 answer

To simplify the expression \((y^{-4} \cdot y^{7})^{7}\), we can start by using the properties of exponents.

Combine the exponents inside the parentheses: \[ y^{-4} \cdot y^{7} = y^{-4 + 7} = y^{3} \]
Now simplify the expression raised to the power of 7: \[ (y^{3})^{7} = y^{3 \cdot 7} = y^{21} \]

Therefore, the simplified form of the original expression \((y^{-4} \cdot y^{7})^{7}\) is:

\[ \boxed{y^{21}} \]