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Simplify the following:
\( \frac{\left(3^{3}\right)^{2} \times 5^{2}}{9^{2} \times 5} \)
Given: $\frac{\left(3^{3}\right)^{2} \times 5^{2}}{9^{2} \times 5}$
Solution:
$\frac{\left(3^{3}\right)^{2} \times 5^{2}}{9^{2} \times 5}$
Cancel the common factor: 5
$=\frac{5\left(3^{3}\right)^{2}}{9^{2}}$
$\left(3^{3}\right)^{2}=3^{6}$
$=\frac{3^{6} \times 5}{9^{2}}$
We know $9^{2}: 3^{4}$
$=\frac{3^{6} \times 5}{3^{4}}$
Cancel common factors :$\frac{5 \times 3^{6}}{3^{4}}: 3^{2} \times 5$
$=3^{2} \times 5$
$3^{2}=9$
$=9 \times 5$
$=45$
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