Fully simplify and write your answer in exponential form with positive exponents only. Example: 153\frac{1}{5^3}

Question

5
3

1
​
not 5−35^{-3}5
−3
.

y−2⋅y−6=y^{-2}\cdot y^{-6}=y
−2
⋅y
−6
=

Answer 1

To simplify \( y^{-2} \cdot y^{-6} \), we can use the property of exponents that states when you multiply two powers with the same base, you add the exponents:

\[ y^{-2} \cdot y^{-6} = y^{-2 + (-6)} = y^{-8} \]

Now, to express this in exponential form with positive exponents only, we can rewrite \( y^{-8} \) using the property that \( a^{-n} = \frac{1}{a^n} \):

\[ y^{-8} = \frac{1}{y^8} \]

Thus, the fully simplified expression is:

\[ \frac{1}{y^8} \]