To solve the expression [tex]\(\frac{8^5}{8^2}\)[/tex], we need to follow these steps:
1. Apply the properties of exponents:
When dividing like bases with exponents, you subtract the exponent in the denominator from the exponent in the numerator.
So, we have:
[tex]\[
\frac{8^5}{8^2} = 8^{5-2}
\][/tex]
2. Simplify the exponent:
Subtract 2 from 5:
[tex]\[
5 - 2 = 3
\][/tex]
Therefore, the expression simplifies to:
[tex]\[
8^{3}
\][/tex]
3. Calculate the value of the simplified exponent:
Now, we need to compute [tex]\(8^3\)[/tex]:
[tex]\[
8^3 = 8 \times 8 \times 8
\][/tex]
4. Compute the multiplication:
Calculate step by step:
[tex]\[
8 \times 8 = 64
\][/tex]
Next, multiply the result by 8 again:
[tex]\[
64 \times 8 = 512
\][/tex]
Thus, [tex]\(\frac{8^5}{8^2} = 8^{3} = 512\)[/tex].
So, the final simplified expression and value is:
[tex]\[
\frac{8^5}{8^2} = 512
\][/tex]
