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


=

1 answer

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:

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

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