To simplify the given expressions, we will apply the laws of exponents.
- For the numerical expression:
\[ 10^6 \cdot 10^2 \cdot 10^{-8} \]
Using the law of exponents that states \(a^m \cdot a^n = a^{m+n}\), we combine the exponents:
\[ 10^{6 + 2 - 8} \]
Calculating the exponent:
\[ 10^{6 + 2 - 8} = 10^{8 - 8} = 10^0 \]
We know from the properties of exponents that \(10^0 = 1\). Thus:
\[ 10^6 \cdot 10^2 \cdot 10^{-8} = 1 \]
- For the expression involving \(s\):
\[ s^{-6} \cdot s^4 \]
Again, using the law of exponents:
\[ s^{-6 + 4} \]
Calculating the exponent:
\[ s^{-6 + 4} = s^{-2} \]
To express \(s^{-2}\) with a positive exponent, we can use the property \(a^{-m} = \frac{1}{a^m}\):
\[ s^{-2} = \frac{1}{s^2} \]
So the simplified forms of the expressions are:
- \(1\)
- \(\frac{1}{s^2}\)