Question

Write the expression for 5 used as a factor eight times being divided by 5 used as a factor six times. Simplify the expression as one power.

Answer 1

To express 5 used as a factor eight times, we can write it as \( 5^8 \). Similarly, 5 used as a factor six times can be written as \( 5^6 \).

Now, we want to divide these two expressions:

\[
\frac{5^8}{5^6}
\]

According to the properties of exponents, specifically the quotient rule, when we divide two powers with the same base, we subtract the exponents:

\[
\frac{5^8}{5^6} = 5^{8-6} = 5^2
\]

So, the simplified expression is:

\[
5^2
\]

Answer 2

Write it normally, with the steps.

Answer 3

Sure! Here are the steps written out normally:

1. **Identify the expressions**:
We need to express 5 used as a factor eight times and divided by 5 used as a factor six times.
- 5 used as a factor eight times is written as \( 5^8 \).
- 5 used as a factor six times is written as \( 5^6 \).

2. **Set up the division**:
We can write this as:
\[
\frac{5^8}{5^6}
\]

3. **Apply the quotient rule for exponents**:
According to the quotient rule, when dividing two expressions with the same base, we subtract the exponents:
\[
\frac{a^m}{a^n} = a^{m-n}
\]
In this case, we have:
\[
\frac{5^8}{5^6} = 5^{8-6}
\]

4. **Simplify the exponent**:
Now, we can simplify the exponent:
\[
8 - 6 = 2
\]
Therefore, we find:
\[
5^{8-6} = 5^2
\]

5. **Final result**:
The simplified expression is:
\[
5^2
\]

So the final answer is \( 5^2 \).