To solve the expression [tex]\(\frac{8^6}{8^5}\)[/tex], follow these steps:
1. Identify that the bases in the numerator and the denominator are the same, which is 8.
2. Recall the properties of exponents: When you divide like bases, you subtract the exponents. This is given by the rule: [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex], where [tex]\(a\)[/tex] is the base, and [tex]\(m\)[/tex] and [tex]\(n\)[/tex] are the exponents.
3. Apply this rule to our given expression:
[tex]\[
\frac{8^6}{8^5} = 8^{6-5}
\][/tex]
4. Simplify the exponent:
[tex]\[
6 - 5 = 1
\][/tex]
5. This results in:
[tex]\[
8^1
\][/tex]
6. Any number raised to the power of 1 is the number itself:
[tex]\[
8^1 = 8
\][/tex]
Therefore, [tex]\(\frac{8^6}{8^5} = 8\)[/tex].
Additionally, the subtraction of the exponents yields:
[tex]\[
6 - 5 = 1
\][/tex]
So the final results are:
- The simplified value of the fraction: [tex]\(8\)[/tex]
- The result of the subtraction of the exponents: [tex]\(1\)[/tex]
Thus, [tex]\(\frac{8^6}{8^5} = 8\)[/tex], and the exponent difference is [tex]\(1\)[/tex].
