Question

Why to the negative power two times Y to the negative power seven times Y to the negative power of two equals what?

Answer 1

To simplify the expression \((-2y^{-7}y^{-2})\), you can follow these steps:

1. **Combine the powers of \(y\)**:
When multiplying two terms with the same base, you can add their exponents:
\[
y^{-7} \cdot y^{-2} = y^{-7 + (-2)} = y^{-9}
\]

2. **Combine with \(-2\)**:
Now, include the coefficient \(-2\):
\[
-2 \cdot y^{-9}
\]

3. **Final result**:
The expression simplifies to:
\[
-2y^{-9}
\]

This can also be expressed in positive exponent form:
\[
-\frac{2}{y^9}
\]

Thus, \((-2y^{-7}y^{-2}) = -2y^{-9} = -\frac{2}{y^9}\).