Question

Simplify using the quotient rule of exponents.
10 to the 5th power times 10 to the second power over ten to the -3 power

Answer 1

To simplify the expression \(\frac{10^5 \times 10^2}{10^{-3}}\), we can use the rules of exponents.

1. **Multiply the powers in the numerator:** According to the product of powers rule, \(a^m \times a^n = a^{m+n}\).

\[
10^5 \times 10^2 = 10^{5+2} = 10^7
\]

2. **Now, rewrite the expression:**

\[
\frac{10^7}{10^{-3}}
\]

3. **Apply the quotient rule of exponents:** According to the quotient of powers rule, \(\frac{a^m}{a^n} = a^{m-n}\).

\[
\frac{10^7}{10^{-3}} = 10^{7 - (-3)} = 10^{7 + 3} = 10^{10}
\]

Thus, the simplified expression is:

\[
10^{10}
\]