Simplify:
`((2^5)^(2)xx7^3)/(8^(3)xx7)`

Answer

To simplify the expression \(\frac{(2^5)^2 \times 7^3}{8^3 \times 7}\), we will follow the steps outlined below:

### Step 1: Apply the Power of a Power Rule
Using the rule \((x^m)^n = x^{m \cdot n}\), we can simplify \((2^5)^2\):
\[ (2^5)^2 = 2^{5 \cdot 2} = 2^{10} \]
So, the expression becomes:
\[ \frac{2^{10} \times 7^3}{8^3 \times 7} \]

### Step 2: Rewrite \(8\) as a Power of \(2\)
Since \(8\) can be expressed as \(2^3\), we can rewrite \(8^3\):
\[ 8^3 = (2^3)^3 = 2^{3 \cdot 3} = 2^9 \]
Now, substitute this back into the expression:
\[ \frac{2^{10} \times 7^3}{2^9 \times 7} \]

### Step 3: Simplify the Expression
Now, we can simplify the expression using the property of exponents \(\frac{x^m}{x^n} = x^{m-n}\):
\[ \frac{2^{10}}{2^9} = 2^{10-9} = 2^1 \]
And for the \(7\) terms:
\[ \frac{7^3}{7} = 7^{3-1} = 7^2 \]
So, the expression simplifies to:
\[ 2^1 \times 7^2 \]

### Step 4: Calculate the Final Result
Now, we can calculate \(2^1\) and \(7^2\):
\[ 2^1 = 2 \quad \text{and} \quad 7^2 = 49 \]
Thus, the final result is:
\[ 2 \times 49 = 98 \]

### Final Answer
The simplified expression is:
\[ \boxed{98} \]