Question

Simplify each expression. Write your answer using a positive exponent.


1
0
6
⋅
1
0
2
⋅
1
0
−
8

=
10
6
⋅10
2
⋅10
−8
=


s
−6

s
4

​
=

Answer 1

To simplify the given expressions, we will apply the laws of exponents.

1. 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:

\[
10^6 \cdot 10^2 \cdot 10^{-8} = 1
\]

2. 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. \(1\)
2. \(\frac{1}{s^2}\)