Answer :

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]