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.
