Answer :

To solve the given fraction:

[tex]\[ \frac{3^3 \times 5^3 \times 7^2}{2^3(7-2)^3} \][/tex]

let's break it down step-by-step.

Step 1: Simplify the denominator's inner expression.

Given:
[tex]\[ (7 - 2)^3 \][/tex]

Calculate inside the parentheses first:
[tex]\[ 7 - 2 = 5 \][/tex]

Then raise this result to the power of 3:
[tex]\[ 5^3 = 5 \times 5 \times 5 = 125 \][/tex]

Step 2: Rewrite the denominator with the simplified inner expression.

The denominator is:
[tex]\[ 2^3 \times 5^3 \][/tex]

Step 3: Calculate [tex]\(2^3\)[/tex].

[tex]\[ 2^3 = 2 \times 2 \times 2 = 8 \][/tex]

Now the denominator becomes:
[tex]\[ 8 \times 125 \][/tex]

Step 4: Simplify the denominator further.

[tex]\[ 8 \times 125 = 1000 \][/tex]

So the denominator is 1000.

Step 5: Simplify the numerator.

Given:
[tex]\[ 3^3 \times 5^3 \times 7^2 \][/tex]

Calculate each term:

[tex]\[ 3^3 = 3 \times 3 \times 3 = 27 \][/tex]

[tex]\[ 5^3 = 5 \times 5 \times 5 = 125 \][/tex]

[tex]\[ 7^2 = 7 \times 7 = 49 \][/tex]

Now multiply these results:

[tex]\[ 27 \times 125 = 3375 \][/tex]

[tex]\[ 3375 \times 49 = 165375 \][/tex]

So the numerator is 165375.

Step 6: Form the simplified fraction with calculated numerator and denominator.

[tex]\[ \frac{165375}{1000} \][/tex]

Step 7: Simplify the fraction if needed.

[tex]\[ \frac{165375}{1000} = 165.375 \][/tex]

Final Answer:

The simplified fraction results in:
[tex]\[ \frac{165375}{1000} = 165.375 \][/tex]

So the fraction [tex]\(\frac{3^3 \times 5^3 \times 7^2}{2^3(7-2)^3}\)[/tex] equals 165.375.