Certainly! Let's solve the expression step-by-step:
Given expression:
[tex]\[
\frac{2^8 \times 3^7}{3^5 \times 2^5}
\][/tex]
### Step 1: Simplify the powers of 2
First, look at the powers of 2 in the numerator and the denominator:
[tex]\[
\frac{2^8}{2^5}
\][/tex]
Apply the properties of exponents (specifically, [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]):
[tex]\[
2^{8-5} = 2^3
\][/tex]
### Step 2: Simplify the powers of 3
Next, look at the powers of 3 in the numerator and the denominator:
[tex]\[
\frac{3^7}{3^5}
\][/tex]
Apply the properties of exponents again:
[tex]\[
3^{7-5} = 3^2
\][/tex]
### Step 3: Combine the simplified terms
Now combine the results of the simplified exponents:
[tex]\[
2^3 \times 3^2
\][/tex]
### Step 4: Calculate the final result
Calculate the actual values of the simplified terms:
[tex]\[
2^3 = 8
\][/tex]
[tex]\[
3^2 = 9
\][/tex]
Now multiply these results together:
[tex]\[
8 \times 9 = 72
\][/tex]
Hence, the final result of the given expression is:
[tex]\[
\boxed{72}
\][/tex]
