Question

Simplify the expression using exponent rules 10 to the fourth power and parentheses times the second power over 10-3 no 10 to the third 10 to the -3rd power times 10 to the fifth power

Answer 1

Let's simplify the expression step by step using the properties of exponents.

The expression seems to be:

\[
\frac{(10^4)^2}{10^{-3} \cdot 10^5}
\]

First, we simplify the numerator:

\[
(10^4)^2 = 10^{4 \cdot 2} = 10^8
\]

Now, we simplify the denominator. For \(10^{-3} \cdot 10^5\), we use the property that \(a^m \cdot a^n = a^{m+n}\):

\[
10^{-3} \cdot 10^5 = 10^{-3 + 5} = 10^2
\]

Now the expression simplifies to:

\[
\frac{10^8}{10^2}
\]

Using the property \( \frac{a^m}{a^n} = a^{m-n} \):

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

Thus, the simplified expression is:

\[
\boxed{10^6}
\]