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 \( 5^2 \).